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 $a+bi$.

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

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

Divide the complex numbers rac{3+2i}{1-i} and express the result in the form $a+bi$.

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

Compute rac{4-7i}{2+3i} and express the answer as $a+bi$.

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

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

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

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

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

Express the product $(4+4i)(-4+4i)$ in polar form rigl( ext{cis } hetaigr), giving $r>0$ and $0\\le heta<2\\pi$.