Solve for z, e ^ (iz) = -1?

r = sqrt ( (-1)^2 ) =1

theta = arctan (y/x) + pi sgn (y) = 0

I get z = 2(k)(pi), k is an integer.

I keep getting a wrong answer. Can anyone help

Update:

The correct answer is 2(k) pi + pi

1 Answer

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  • xyzzy
    Lv 7
    6 years ago
    Favorite Answer

    e^&pi&i = -1

    it is one of the beautiful equations in mathematics.

    e^ix = cos x + i sin x

    cos x = -1

    x = (2n+1) π

    θ = arctan (y/x) + 2n π is correct. I don't know why you have sgn (y) in your formula.

    anyway.. with x = -1 draw it out and look at where θ has to be..

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