Tuesday

October 21, 2014

October 21, 2014

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

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 6:53pmtan(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(...

homework !! - My daughter did excellent in school last year (grade 1) She was ...

Pre Calculus - So I only have 3 homework questions left and I can't seem to ...

English - I still have the following doubts. I really hope you can help me this ...

help me please - today has been very hectic along with homework i found out ...

Pre-Calc - Can you show me how to find the rectangular equation of r=2costheta...

pschology - An article published in the "New York Times" reported the results of...

english - The essay has to be 350 words What I learned in Home School Home ...