How do you add subtract multiply and divide complex numbers and polynomials
Final answer:
To operate on complex numbers, add or subtract real and imaginary parts separately, multiply using the distributive property, and divide by multiplying by the conjugate of the denominator. Polynomial operations similarly involve combining like terms, using the distributive property, and performing long or synthetic division.
Explanation:
Adding, Subtracting, Multiplying, and Dividing Complex Numbers and Polynomials
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2i + 4i) = 4 + 6i. For subtracting complex numbers, similarly subtract the real and imaginary parts: (3 + 2i) - (1 + 4i) = (3 - 1) + (2i - 4i) = 2 - 2i.
To multiply complex numbers, use the distributive property (FOIL), and remember that i² = -1. For instance, (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i² = 3 + 14i - 8 = -5 + 14i.
For dividing complex numbers, multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. For example, (3 + 2i) ÷ (1 + 4i), multiply numerator and denominator by (1 - 4i) to get [(3 + 2i)(1 - 4i)] ÷ [(1 + 4i)(1 - 4i)] = (3 - 12i + 2i - 8i²) ÷ (1 - 16i²) = (11 - 10i) ÷ 17 = (11÷ 17) - (10i÷ 17).
Polynomial operations are similar, but instead of imaginary units, we work with variables. For adding polynomials, combine like terms. For subtracting polynomials, change the sign of each term in the polynomial being subtracted and combine like terms. Multiplying polynomials also requires the distributive property, and for division, you can use either long division or synthetic division depending on the polynomials involved.
Plz help any1 plzzzzzzzzzz!!!!!!!!!!!!!!!!!
Hermina cut a 10" by 15" piece of cardboard down the diagonal
Hermina can calculate the length of the diagonal on her 10" by 15" rectangle of cardboard by using the Pythagorean theorem. The formula states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides, the length and the width. Thus, by inputting the values into the formula, we get a diagonal length of about 18.03".
Explanation:The question involves calculating the length of the diagonal on a rectangular piece of cardboard. In mathematics, the Pythagorean theorem is used to calculate the length of a diagonal. In this case, the length and width of the rectangle are given as 10" and 15" respectively. We can apply the theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The diagonal here acts as the hypotenuse, with the other two sides being the length and width of the rectangle. Therefore, the length of the diagonal is the square root of the sum of squares of these sides, which would be sqrt(10^2 + 15^2), resulting in approximately 18.03".
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Joy Co. allocates overhead expenses to all departments on the basis of floor space (sq. ft.) occupied by each department. This year total overhead expenses were $22,000. Department A. occupied 15,000 sq. ft., Department B. 18,000 sq. ft., and Department C. 9,000 sq. ft. The amount of overhead allocated to Department B is (round to the nearest dollar):
Can someone please help me? person who helps gets brainly
−5r+8r+5
What is the solution to this system of equations?
Hilary wants to fill a mini cake pan with batter to make a mini cake for Phillip's party. The cake pan is 4.0 inches long, 9.0 inches wide, and 2.2 inches deep. What is the volume of the cake pan?
The volume of the cake pan Hilary wants to use is calculated using the formula for the volume of a rectangular prism. With dimensions of 4.0 inches by 9.0 inches by 2.2 inches, the volume is 79.2 cubic inches.
To find the volume of the cake pan that Hilary wants to use for making a mini cake for Phillip's party, we need to use the formula for the volume of a rectangular prism, which is Volume = length × width ×height. Given the dimensions of the cake pan are 4.0 inches long, 9.0 inches wide, and 2.2 inches deep, we can calculate the volume as follows:
Volume = length × width × height
Volume = 4.0 in× 9.0 in × 2.2 in
Volume = 79.2 in³
Therefore, the volume of the cake pan is 79.2 cubic inches.
NEED HELP FAST!
3.
(08.01 MC)
The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B? (1 point)
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answer:
(3,4) For both
Both lines meet up at that point. X is the thicker ones in the middle going across the graph while y is upward.
(x,y)
Choose the correct simplification of x to the 2nd power over y to the 5th power all raised to the 4th power. (5 points)
x to the 8th power over y to the 9th power
y12
x12y8
x to the 8th power over y to the 20th power
What is the verbal expression of 23f
Round this number to the nearest 1,000 25,386
Round this number to the nearest 100,000 5,370,288
Round this number to the nearest 10,000 7,298,341
Round this number to the nearest 1,000,000 6,289,002
I know thi is a lot but please pretty pleas this is the hardest one:(
A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the special character is at the end of the password, how many possibilities are there? a. 175,760
1st character = 26 possibilities ( 26 letters in the alphabet)
2nd character = 26 possibilities
3rd character = 26 possibilities
4th character = 10 ( 10 special characters)
26 x 26 x 26 x 10 = 175,760 combinations
b(n)=4−6(n−1) Find the 4th term in the sequence.
Answer:
-14
Step-by-step explanation:
answer on khan
Olga saves $15 from every paycheck to save up for a new game system that cost $399. Currently, she has $360 saved. Ignoring the purchase, how many more paychecks does she have until she has enough money saved to buy the game system
(sint+cost)^2=
A.) 1
B.) 1+2sint
C.) 1+sin2t
D.) sin(t^2)+cos(t^2)
E.) sin(t^2)+2sintcost+cos(t^2)
An elephant can run one over four mile in 36 seconds. Which of the following correctly shows this rate as miles per hour?
thirty-six seconds over one-fourth mile = 25 miles per hour
one-fourth mile over thirty-six seconds = 144 miles per hour
one-fourth mile over thirty-six seconds = 25 miles per hour
thirty-six seconds over one-fourth mile = 144 miles per hour
Answer:
The answer is 1/4 mile over 36 seconds = 24 miles per hour
Step-by-step explanation: I hope this helps :)
A factory used 396.25 pounds of tomatoes to make 6.25 batches of salsa. How many pounds of tomatoes were used in each batch?
Answer:
63.4 pounds of tomatoes were used in each batch
Step-by-step explanation:
A factory used 396.25 pounds of tomatoes to make 6.25 batches of salsa.
Or, In 6.25 batches of salsa 396.25 pounds of tomatoes were used.
In 1 batch of salsa , [tex]\dfrac{396.25}{6.25}[/tex] pounds of tomatoes will be used.
i.e. In 1 batch of salsa , 63.4 pounds of tomatoes will be used.
Hence, 63.4 pounds of tomatoes were used in each batch
How can you use the number line in picture it to figure out how many miles Tim travels from home to school
identify the following probability as theoretical or empirical. After tossing the same coin 10 times, you are surprised to find that tails has come up 8 times. You therefore conclude that this coin is not fair and that the probability of getting tails with this coin is 0.80. A. Empirical B. Theoretical
Answer:
A. Empirical
Step-by-step explanation:
Theoretical probability is defined as a probability which is based on reasoning. This is written in a ratio form - of the number of favorable outcomes to the number of possible outcomes.
And the empirical probability gives an estimation of an event occurring based on how often that event occurred after collecting the data from large number of trials.
So, based on the definitions, the given scenario is empirical or experimental probability.
Multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). Express the answer in scientific notation. 9.6 ⋅ 1021 9.6 ⋅ 1022 96 ⋅ 1021 96 ⋅ 1022
Answer:
9.6 × [tex]10^{21} )[/tex].
Step-by-step explanation:
Given : Multiply [tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
To find : Express the answer in scientific notation.
Solution : We have given that
[tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
Combine the like terms
(2.4 * 4 )( [tex](10^{14} ) (10^{7} )[/tex].
By the exponent same base rule : if the base of two exponent are same then exponent will be add.
9.6 × [tex]10^{14 + 7} )[/tex].
9.6 × [tex]10^{21} )[/tex].
Therefore, 9.6 × [tex]10^{21} )[/tex].
Write 12c+10 as an equivalent expression with one term
A figure has a vertex at (-1, -3). If the figure has line symmetry about the y-axis, what are the coordinates of another vertex of the figure?
A) (-3, -1)
B) (3, 1)
C) (1, -3)
D) (-1, 3)
Answer:
(1,-3)
Step-by-step explanation:
A figure has a vertex at (-1, -3). If the figure has line symmetry about the y-axis, find the coordinates
When a vertex is reflected over y axis then the value of y remains the same , the x value becomes -x
for (x,y) reflected over line symmetry y axis
(x,y) becomes (-x,y)
So the vertex (-1,-3) becomes (1,-3)
a fellow classmate tosses 4 coins and finds that 3 of them come up tails. Which of the following is the best conclusion for her to come to?
A. She needs to keep flipping the coins until she gets a 50% in heads to determine if they are fair.
B. The coins are unfair
C. This could easily happen with a fair coin after only 4 flips
D. If she flips the coins one more, they will all come up heads
Answer:
Option C -This could easily happen with a fair coin after only 4 flips.
Step-by-step explanation:
Given : A fellow classmate tosses 4 coins and finds that 3 of them come up tails.
To find : Which of the following is the best conclusion for her to come to?
Solution :
According to statement,
A fellow classmate tosses 4 coins and finds that 3 of them come up tails.
This could be happen when coin is tossed or flip 4 times and the coin must be fair.
As when we flip 4 coins the possible outcomes were
HHHH THHH HTHH TTHH
HHHT THHT HTHT TTHT
HHTH THTH HTTH TTTH
HHTT THTT HTTT TTTT
So, The best conclusion for her is Option C
This could easily happen with a fair coin after only 4 flips.
At Mei's Printing Company LLC there are two kinds of printing presses: Model A which can print 80 books per day and Model B which can print 30 books per day. The company owns 10 total printing presses and this allows them to print 400 books per day. How many of each type of press do they have?
Subtract the fractions and simplify the answer 13/15 -2 2/3
2 2/3 = 8/3
8/3= 40/15
13/15 - 40/15 = -27/15 = -1 12/15
the area of a circle of radius 10 units is equal to the surface area of a sphere of radius 5 units. True or false?
The average number of rainy days in Seattle, Washington is listed below: Month January February March April Rainy days 18 16 17 14 If the data was only accurate to the tens place, which month's rainy day total would be different from the others?
Answer: April's rainy days are different from the others.
Step-by-step explanation:
Since we have given that
Months Rainy days
January 18
February 16
March 17
April. 14
When we round the rainy days to nearest tens then we get that
January has 20 rainy days
February has 20 rainy days.
March has 20 rainy days.
But April has 10 rainy days.
So, April's rainy days is different from others.
5+ 1/7b = -2
whats be and explanation
(don't get it cause its a fraction)
Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same hole in six hours. How long will it take them if they worked together?
Explain too please, thanks.
Lily is 14 older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined she?
The combined age of Lily and Ezekiel is 42.
Lily is 14 older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined To be determined.
In mathematics it deals with numbers of operations according to the statements.
Let the age of lily be L and the gare of her brother Ezekiel is E.
Lily is 14 older than her little brother Ezekiel.
L = 14 + E - - - - - -(1)
In 8 years, Lily will be twice as old as Ezekiel will be then.
L = 2(E)
put L in equation 1.
2E = 14 + E
2E - E = 14
E = 14
Now put E in equation 1
L = 14 + 14
L = 28
Combined age of Lily and Ezekiel's = 28 + 14
= 42
Thus, the combined age of Lily and Ezekiel's is 42.
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