Question Type 6: Applying powers to complex numbers in Euler form Exercises

Calculate $(5e^{i\pi/2})^3$ and express the result in $a+bi$ form.

Find $(\sqrt{2}e^{i3\pi/4})^2$ and express the answer in Euler form.

Compute $(3e^{i2\pi/5})^5$ and give the result in Euler form.

Compute $(2e^{i\pi/6})^5$ and give your answer in Euler form.

Evaluate $(e^{i\pi/3})^6$ and simplify fully.

Calculate $(3e^{-i\pi/4})^4$ and write the answer in $a+bi$ form.

Compute $(4e^{-i\pi/3})^3$ and express the result in $a+bi$ form.

Calculate $(2e^{i\pi/3})^{-2}$ and express the result in $a+bi$ form.

Let $z=5e^{i\pi/5}$. Find $z^8$ and write your answer in modulus–argument form with the argument in $(-\pi,\pi]$.

Find the modulus and argument of $(6e^{i3\pi/4})^3$, giving the argument in $(-\pi,\pi]$.

Evaluate $(\tfrac12 e^{i\pi/7})^7$ and express your answer in $a+bi$ form.

For $w=7e^{i2\pi/3}$, compute $w^{-3}$ and simplify the argument to the principal value in $(-\pi,\pi]$.