How do you simplify # (3+3*sqrt3 i)^4#?
Here are the steps required for Multiplying Complex Numbers:
Step 1: Distribute (or FOIL) to remove the parenthesis.
Step 2 : Simplify the powers of i, specifically remember that i2 = –1.
Step 3 : Combine like terms, that is, combine real numbers with real numbers and imaginary numbers with imaginary numbers.
Prerequisite : D'Moivre's Theorem :
has readily derived!
=>3^4 (1 + 2 sqrt3 i + 3 i^2)^2#