# Math

use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form.

(2+2i)^6

a=2 b=2 n=6

r=sqrt 2^2 + 2^2 = sqrt8
Q=7pi/4

(sqrt8)^6 = 512
512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4
512 (cos 21pi/2) + i sin (21pi/2)
512(cos pi/2) + i (sin pi/2)
512(2+2i)

1024 + 1024i

Is this correct?

1. 👍 0
2. 👎 0
3. 👁 106
1. i=253

1. 👍 0
2. 👎 0
posted by gorge
2. Rewrite (2+2i)^6 as

[2^3/2*(cos pi/4 + i sin pi/4)]^6
= 2^9*[cos 6pi/4 * i sin 6pi/4]
= 512* i sinpi/2
= -512 i

I see several error in your derivation.

1. 👍 0
2. 👎 0
posted by drwls
3. Where did you get the angle of 7π/4 ?

I get an angle of π/4

check:
√8(cos π/4 + i sin π/4_
= √8(1/√2 + i (1/√2)
= 2 + 2i

so by De Moivre's Theorem
(2+2i)^6
= √8^6(cos (6π/4) + i sin (6π/4))
= 512( + i(-1))
= - 512i

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### precalculus

Use Demoivre's theorem to find the indicated power of the complex number. Write the result in standard form. 1.(3(cos5pi/4+i sin 5pi/4))^8 2.(3-3i)^6

asked by Susan on November 26, 2016
2. ### Calc

Use DeMoivre's Theorem to find the indicated power of the following complex number (-6 + 6i)^4 Please help, i don't get this guys therom at all...

asked by Janique on February 13, 2012
3. ### Math

use Demoivre's Theorem to find the indicated power of the complex number. Express the result in standard form. (2+2i)^6 a=2 b=2 n=6 r=sqrt 2^2 + 2^2 = sqrt8 Q=7pi/4 (sqrt8)^6 = 512 512(cos 6/1 x 7pi/4) + i sin 6 x 7pi/4 512 (cos

4. ### precal 2

use Demoivre's theorem to find the power [5(cos3.2 + isin3.2)]^4

asked by qui qui on July 31, 2011
5. ### Pre-calculus

I am having difficulty with two problems: 1) Evaluate (1+i)^12 by using DeMoivre's Theorem. Express the result in rectangular form. So far I have: r=sqrt(1)^2+(1)^2 which simplified is sqrt2. Don't know how to proceed. 2) Write

asked by Lucy on September 30, 2008
6. ### Math/Standard and scientific notation

Express each measure in standard form. (One more thing by the way you need this few prefixes) Tera= 10 to the 12th power Giga= 10 to the 9th power Mega= 10 to the 6th power Kilo= 10 to the 3rd power Pico= 10 to the -12th power

asked by Sandy on February 25, 2009
7. ### Pre-Calculus

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

asked by Anne on October 10, 2011
8. ### calculus

Use the demoivre's theorem to find the answer? (1+i)^8

asked by mimi on May 20, 2011
9. ### precal

how do you use demoivre theorem for (-1+i)^7

asked by LK on March 15, 2015
10. ### precal

demoivre theorem (2-2i)^8

asked by LK on March 15, 2015

More Similar Questions