# Thread: complex numbers-exponential form and solving equations

1. ## complex numbers-exponential form and solving equations

1) a) Write -8 in exponential form.
b) Solve the equation z^4 = −8. (give your answers with real and imaginary parts).
2) Solve z^3 = 1 + i (leave your answers in the trigonometric form)
3) Solve z^2 = (√3) − i. (give your answers with real and imaginary parts).

2. ## Re: complex numbers-exponential form and solving equations

Originally Posted by heejenna55
1) a) Write -8 in exponential form.
b) Solve the equation z^4 = −8. (give your answers with real and imaginary parts).
2) Solve z^3 = 1 + i (leave your answers in the trigonometric form)
3) Solve z^2 = (√3) − i. (give your answers with real and imaginary parts).
Here is basic help.
Let $\displaystyle \exp(i\theta)=\cos(\theta)+i\sin(\theta)$.
$\displaystyle - 8 = 8\exp \left( {\pi i} \right)$

$\displaystyle 1 + i = \sqrt 2 \exp \left( {\frac{{\pi i}}{4}} \right)$

$\displaystyle \sqrt 3 - i = 2\exp \left( {\frac{{-\pi i}}{6}} \right)$