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To review, the square root of a negative number is non-real, or an imaginary number. The imaginary unit i is defined as the square root of -1.
If you were to square both sides of this equation, you would have i^2 on the left side, and -1 on the right side, so you also know that is equal to -1.
A complex number is a value in the form below, in which a and b are real numbers, and i is the imaginary unit.
When multiplying complex numbers, use the FOIL method, because of the addition or subtraction that occurs between the real and imaginary parts of complex numbers. Therefore, multiplying complex numbers together is similar to multiplying binomials together.
EXAMPLE
Suppose you want to multiply the following complex numbers.Source: This work is adapted from Sophia author Colleen Atakpu.