What are the real and imaginary parts of the complex number $5i$?

Compute $(3-2i)+(-5+7i)+(1+4i)$ and simplify to standard form.

Simplify $\sqrt{-200}$ fully by extracting perfect-square factors.

Which value is $i^6$ equal to?

In a simple AC circuit, impedances are sometimes represented as complex numbers and combine multiplicatively in series. Compute the product $(2+3i)(4-i)$, representing the combination of impedances, and express the result in $a+bi$ form.

Compute $\frac{1+2i}{3-4i}$ in standard form $a+bi$, reduced to lowest terms.