Algebra
# Complex Numbers

What is the absolute value of the complex number \[12+5i?\]

**Details and assumptions**

\(i\) is the imaginary number that satisfies \(i^2 = -1\).

Is it true that \(\Re\big(\Im(z)\big) = \Im\big(\Re(z)\big)\) for all complex numbers \(z?\)

What is the value of \[ \left(9 + \sqrt{-81}\right)\left(20 - \sqrt{-400}\right)? \]

Simplify \(\frac{4+2i}{2-i}\).

**Details and assumptions**

\(i\) is the imaginary number that satisfies \(i^2 = -1\).

Which set of complex numbers satisfy the equation \(iz + \overline{z} = 0\)?

Hint: Start by letting \(z = x + iy\).

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