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Gennadij [26K]
3 years ago
13

Hi, I am new to this website :) I'm currently taking an online trig class on De Moivre's theorem and I don't understand it at al

l! The question is: Write each expression in the standard form for a complex number, a+bi.
1. [3cos(27))+isin(27)]^5
2. [2(cos(40))+isin(40)]^6
any info regarding this question would be extremely helpful! Thanks!
Mathematics
1 answer:
Vladimir [108]3 years ago
7 0
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.

For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes

[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))] 

it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.

For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)

[2^6(cos(40*6))+isin(40*6)],

[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)

And the answer is -32 -32 √3 i

Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i

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Help please asap PLEASE TELL ME THE WORKING AS WELL.​
DanielleElmas [232]

Answer:

a = 9 / 7

step by step explanation:

9 / - a + 15 = 8

Determined the defined range

9 / ( - a ) + 15 = 8 , a ≠ 0

subtract 15 from each side

9 / - a + 15 - 15 = 8 - 15

calculate the difference

9 / - a = - 7

multiply both side of equation by - a

9 / - a × - a = - 7 × - a

9 = 7 a

divide each side by of equation by -7

9 / 7 = 7 a / 7

9 / 7 = a

swap the side of equation . ( optional )

a = 9 / 7

6 0
3 years ago
Read 2 more answers
Please help! [99 points]
anygoal [31]
This is a linear function.

A linear function is a straight line that has a slope, and follows the formula: <em>
y = mx + b</em>

In which: 
y = y
m = slope
x = x
b = y -intercept


hope this helps<em />
4 0
3 years ago
Read 2 more answers
The cost of 9 cupcakes is $12.50. What is the equation that represents The cost y of x amount of cupcakes What is the cause of 2
zubka84 [21]

Answer:

$33.33

Step-by-step explanation:

9--->12.50

24---->y

y=12.50x24/9

y=33.33

6 0
3 years ago
A rectangular hotel room is 11 feet wide and 25 feet long. What is its perimeter?
bekas [8.4K]

Answer:

The answer is 72

Step-by-step explanation:

The formula for perimeter is (L+W)x2

So in your case (11+25)x2

Or add all 4 sides of the rectangle up and you have your answer <3

5 0
2 years ago
Which expression is equivalent to (-7) (-7) (-7)
Virty [35]
I think the answer is -7x(-7)x(-7)
5 0
3 years ago
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