Imaginary Numbers

What does i² simplify to?

-1

what does sqrt(-16) simplify to?

4i

What is a complex number?

Number that has both imaginary and real numbers inside of it.

What does i^51 simplify to?

-i

Complex Conjugate

Conjugate where the real component remains the same, while the imaginary component is equal but opposite.

Fundamental Theorem of Algebra

Every one-variable polynomial equation has at least one complex root.

Amount of complex roots for a quadratic expression

A quadratic expression has two complex roots.

Amount of complex roots for a quintic expression

Five complex roots

Modulus Formula

c² = a² + b²

imaginary value axis location

y-axis

When a complex number is being divided by another complex number…

Multiply the fraction by the denominator’s complex conjugate