Question Type 4: Multiplying and dividing complex numbers in Cartesian form Bootcamps

Calculate $(4-5i)(4+5i)$ and give the answer in the form $a+bi$.

Compute $(1+i)(1-i)$ and express in simplest form.

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

Evaluate the quotient $\displaystyle \frac{3+2i}{1-i}$ and express in the form $a+bi$.

Given $z_1=2-i$ and $z_2=-1+3i$, find the product $z_1\times z_2$ in the form $a+bi$.

Given $z=-3+4i$, compute $z\cdot\overline{z}$ and give the result as a real number.

Find the product $(2-7i)(-3+4i)$ and write the result in the form $a+bi$.

Find $\displaystyle \frac{5-3i}{2+i}$ in the form $a+bi$.

Divide $z_1=4+3i$ by $z_2=1-2i$ and express the result in the form $a+bi$.

Compute $\displaystyle \frac{1+2i}{2-3i}$ and express the answer in the form $a+bi$.

Find $\displaystyle \frac{(1+i)^3}{1-i}$ in the form $a+bi$.

Compute $\displaystyle \frac{(2+3i)(-1+4i)}{3-2i}$ and express your answer in the form $a+bi$.