Question Type 4: Applying multiplication and division to complex numbers in Euler form Exercises

Multiply $4e^{i\pi/2}$ by $e^{i\pi/3}$ and give the result in Euler form.

Multiply $2e^{i\pi/6}$ by $3e^{i\pi/3}$ and express the result in Euler form.

Compute $\displaystyle\frac{8e^{-i\pi/6}}{2e^{-i\pi/2}}$ in Euler form.

Compute $\displaystyle\frac{5e^{i\pi/2}}{8e^{i\pi/4}}$ and express the answer in Euler form.

Compute $\displaystyle\frac{6e^{-i\pi/3}}{3e^{i\pi/4}}$ and express the result in Euler form.

Compute $\displaystyle\frac{7e^{i4\pi/5}}{5e^{i9\pi/10}}$ and express the result in Euler form.

Multiply $2e^{i\pi/6}\times3e^{-i\pi/4}\times4e^{i\pi/3}$ and express your answer in Euler form.

Compute $\displaystyle\frac{5e^{i7\pi/4}}{4e^{i3\pi/2}}$ and express the argument in the principal range $(-\pi,\pi]$.

Multiply $7e^{i5\pi/4}$ by $2e^{i2\pi/3}$ and express the result in Euler form.

Multiply $5e^{i2\pi/3}\times3e^{i5\pi/6}$ and then convert the result to $a+bi$ form.

Simplify $\displaystyle\frac{3e^{i\pi/3}}{6e^{-i\pi/4}}\times2e^{i\pi/12}$ and express the answer in Euler form.

Simplify $\displaystyle\frac{6e^{i3\pi/2}\times4e^{-i\pi/6}}{2e^{i\pi/3}}$ and express your answer in $a+bi$ form.