Complex Number Question - Euler's Formula?

[KAISER91]

Complex Number Question - Euler's Formula?

Homework Statement

Express (-2 + 2i)^10 in the form re^(iθ)

Homework Equations

Euler's Formula, I think?

The Answer given is: (2√2)^10 e^[i(15pi/2)]

The Attempt at a Solution

I don't know what I'm doing wrong here;

r = √[(-2)^2 + 2^2] = √8 = 2√2theta = pi - arctan (y/x)

= pi - arctan (2/-2)

= pi - 45

= pi - (pi/4)

= 3pi / 4Help will be appreciated. Thanks

 

[╔(σ_σ)╝]

Well for one thing you didn't raise your r and theta to the power of 10.

(re^(ix))^10= r^10(e^(i(10x)). Your next step should be to reduce 10x to a smaller angle since angles repeat after 2pi.

Hope that helps.

If you need more explainatiom post again. :-):-)

 

[KAISER91]

Well for one thing you didn't raise your r and theta to the power of 10.

(re^(ix))^10= r^10(e^(i(10x)). Your next step should be to reduce 10x to a smaller angle since angles repeat after 2pi.

Hope that helps.

If you need more explainatiom post again. :-):-)

Thanks for the reply mate.

So I have to raise r and theta to ^10.

That makes r = (2√2)^10

However how did theta become 15pi/2 ?

 

[KAISER91]

I think I got it.

Just bring down 10 as the power??

e^[10 x i(3pi/4)]

 

[╔(σ_σ)╝]

Yes and then simplify the angle. For example 7pi is the same as pi + 2(3)pi.

The answer you gave is correct but was not put in the "best" way.

So 10/4(3pi) = 15pi/2 = 7pi + pi/2 = 6pi + 3pi/2

Angles in polar form are usually written as i( theta + 2npi) :-)

We usually do not put the 2npi part since it is "implied" thus, your answer should be

e^(i 3/2(pi))

 

[KAISER91]

Yes and then simplify the angle. For example 7pi is the same as pi + 2(3)pi.

The answer you gave is correct but was not put in the "best" way.

So 10/4(3pi) = 15pi/2 = 7pi + pi/2 = 6pi + 3pi/2

Angles in polar form are usually written as i( theta + 2npi) :-)

We usually do not put the 2npi part since it is "implied" thus, your answer should be

e^(i 3/2(pi))

OH!

I understand now. Thanks heeps for the help.