Express the following in the form $\frac{(a-ib)}{c}$, then $c=$

$\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}$

Express the following in the form $\frac{a+ib}{c}$, then find $c=$

$\frac{(2+3i{)}^2}{(2-i)}$

Express the following in the form $(\mathrm{a}+\mathrm{ib})$ then $a=$

$\frac{(1-i{)}^3}{\left(1-i^3\right)}$

Express each of the following in the form $\left(\frac{\mathrm{a}+\mathrm{ib}}{c}\right)$, then $c=$

$\frac{(1+2i{)}^3}{(1+i)(2-i)}$

Simplify each of the following and express it in the form $\frac{(\mathrm{a}+\mathrm{ib})}{c}$, then $c=$

$\left(\frac{5}{-3+2i}+\frac{2}{1-i}\right)\left(\frac{4-5i}{3+2i}\right)$

Simplify the following and express it in the form $\left(\frac{a+ib}{c}\right)$, then $c=$

$\left(\frac{1}{1+4i}-\frac{2}{1+i}\right)\left(\frac{1-i}{5+3i}\right)$

Show that $\left\{\frac{(3+2i)}{(2-3i)}+\frac{(3-2i)}{(2+3i)}\right\}$is purely real.

Show that $\left\{\frac{(\sqrt{7}+i\sqrt{3})}{(\sqrt{7}-i\sqrt{3})}+\frac{(\sqrt{7}-i\sqrt{3})}{(\sqrt{7}+i\sqrt{3})}\right\}$is purely real.