Question Type 6: Performing multiplication and division on complex numbers Exercises

Multiply the complex numbers $(2+3i)$ and $(4-5i)$, and express the result in the form $a+bi$.

Compute $\frac{4-7i}{2+3i}$ and express the answer in the form $a+bi$.

Find $\frac{5+5i}{2 - i}$ in the form $a+bi$.

Express the complex number $\frac{3+2i}{1-i}$ in the form $a+bi$, where $a, b \in \mathbb{R}$.

Calculate $(4+3i)(5-6i)$ and express the result in the form $a+bi$.

Simplify the power $(1+i)^3$ and express the result in the form $a+bi$.

Find the product $(1 - 2i)(3 + 4i)$ and write your answer in the form $a + bi$.

Find the complex number $z$ such that $z(1-2i)=5+5i$, and express $z$ in the form $a+bi$.

Calculate the product $(2-3i)(-1+4i)(3+i)$ and write your answer in the form $a+bi$.

Given $z=7\,\text{cis}\left(\frac{\pi}{3}\right)$ and $w=2\,\text{cis}\left(\frac{\pi}{4}\right)$, compute $\frac{z}{w}$ and express your answer in polar form.

Multiply $(2+2i)$ by $(1-3i)$ and represent the points for $2+2i$, $1-3i$, and the product on an Argand diagram.

Express the product $(4+4i)(-4+4i)$ in polar form $r(\text{cis } \theta)$, where $r > 0$ and $0 \le \theta < 2\pi$.