9. Roots, Radicals, and Complex Numbers

Perform the indicated operation. Express your answer in standard form.

${(3+8i)}^2$

Find the product. Express your answer in standard form.

$2i(9-4i)(6+5i)$

Multiply the following and simplify.

$(5-i)\left(12\right)$

Multiply the following and simplify.

$\left(13i\right)\left(17i\right)$

Multiply the following and simplify.

$(7+3i)(7-3i)$

Find the product of the given complex number and its conjugate.

$4-5i$

Find the product of the given complex number and its conjugate.

$-7-i$

Find the quotient. Express your answer in standard form.  

$\frac{6+i}{4-2i}$

Find the quotient. Express your answer in standard form.

$\frac{-5+3i}{-7-4i}$

Evaluate the following powers of $i$.

${\left(3i\right)}^4$

Evaluate the following powers of $i$.

${\left(4i\right)}^{-3}$

Simplify the power of $i$.

$i^{1003}$

Simplify the power of $i$.

$i^{85}$