Question

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.
\[\frac{ 3-2i }{ 1+4i }\]

Answer 1

Do you know what the conjugate of the denominator is?

Answer 2

nope

Answer 3

change the sign in front of the imaginary part, so the conjugate is 1-4i.
multiply both numerator and denominator by it to get rid of the i in the denominator.
\[\frac{ (3-2i)(1-4i) }{ (1+4i)(1-4i) }\]

Answer 4

then foil both