Math

posted by .

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?

  • Math -

    i=253

  • Math -

    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.

  • Math -

    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

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math Help please!!

    Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine …
  2. Algebra

    Two more I would like to check my work on: Solve using the square root property: (x+6)^2 = 4 x+6 = sqrt4 x+6 = -sqrt4 x+6 = 2 x+6 = -2 x+6-6 = 2-6 x+6-6 = -2-6 x = 4 x = -8 Solve by completing the square: x^2+6x+1=0 x^2+6x+1-1 = 0-1 …
  3. 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 the …
  4. Calculus

    Hi. In an integration solution, the integral of (1/(sqrt (8-u squared)) is written as arcsin(u/sqrt 8), but I don't see how they got it. When I did it I got (1/8)*(arcsin(u*sqrt8)). What I did was take sqrt8 common in the denominator …
  5. 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) …
  6. math

    Perform the indicated operation(s) and express the result in standard form. Leave answers in terms of square roots (do not use decimals). (-9-sqrt-3)^2
  7. college algebra

    Perform the indicated operation(s) and express the result in standard form. Leave answers in terms of square roots (do not use decimals). (-9-sqrt-3)^2
  8. 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...
  9. Algebra

    Given that 2^x+2^x+2^x+2^x=512, what is the value of x?
  10. 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

More Similar Questions