Posted by **Anne** on Monday, October 10, 2011 at 5:35pm.

Could someone help me with this-we learned this today in school but I'm not getting it now that I'm home with my homework-I have lots of these to do can someone help with this one and then maybe it'll click-thank you

Find (sqrt3/2 -1/2i)^4 by using DeMoivre's Theorem

I have to convert to polar, use the theorem and put it back into rectangular form

- Pre-Calculus -
**Steve**, Monday, October 10, 2011 at 6:53pm
tan(t) = y/x = (-1/2) /(sqrt(3)/2) = -1/sqrt(3)

so, t = -pi/6

r^2 = x^2 + y^2 = 3/4 + 1/4 = 1

r = 1

so, point z = (1,-pi/6)

z^4 = 1^4 cis 4*(-pi/6) = 4 cis -2pi/3

x = r cos -2pi/3 = 1 * -1/2

y = r sin -2pi/3 = 1 * -sqrt(3)/2

z^4 = (-1/2, -sqrt(3)/2)

Just for confirmation,

(sqrt(3)/2 - i/2)^4 =

9/16 - 4*3*sqrt(3)/(8*2)i + 6*3/4*1/4 i^2 - 4*sqrt(3)/2 * 1/8 i^3 + 1/16 i^4

= 9/16 - 3sqrt(3)/4 i - 18/16 + 1/4 sqrt(3) i + 1/16

-8/16 - sqrt(3)/2 i

## Answer this Question

## Related Questions

- Grammar - Write one paragraph (150 word minimum) about the most helpful ...
- English - 1. I have hunger to go home now. 2. I have a hunger to go home now. 3...
- Pre-Calculus - Can you show me how to find the rectangular equation: r=2cos(...
- Pre-Calculus/Calculus - I am too embarassed to ask this Calculus (really pre-...
- Chemistry - Unfortunately I was hit by the sweep of illnesses going around due ...
- Foreign languages - Can you please check these sentences, too? Thank you. 1) My ...
- algebra - We just learned equations & inequalities today and im so confused on ...
- sci 241 - i have to ask this queation to someone and no one is at my home right ...
- Calculus - a populatioin of bacteria has an initial size of 500. the population...
- writing - is this essay persausive and can you check and fix any mistake topic ...