IB Mathematics Applications & Interpretation Question Type 4: Applying Multiplication and Division to Complex Numbers in Euler Form Exercises

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

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

Simplify $\frac{3e^{i\pi /3}}{6e^{-i\pi /4}}\times 2e^{i\pi /12}$ and express the answer in Euler form.

Simplify $$\frac{6e^{i\frac{3\pi }{2}}\times 4e^{-i\frac{\pi }{6}}}{2e^{i\frac{\pi }{3}}}$$ and express your answer in $a+bi$ form.

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

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

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

Multiply $5{\mathrm{e}}^{\mathrm{i}\frac{2\pi }{3}}\times 3{\mathrm{e}}^{\mathrm{i}\frac{5\pi }{6}}$ and express the result in the form $a+b\mathrm{i}$, where $a,b\in \mathbb{R}$.

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

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

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

Multiply $7e^{i5\pi /4}$ by $2e^{i2\pi /3}$ and express the result in Euler form $r{e}^{i\theta }$, where $-\pi <\theta \le \pi$.