Question

Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.


`(3-2i)/(1+4i)`

Answer 1

(-5/17) +(-14/17)i

Explanation:

You want the simplified form of (3-2i)/(1+4i).

Simplification

A fraction with a complex denominator can be made to have a real denominator by multiplying both numerator and denominator by the conjugate of the denominator.

`(3-2i)/(1+4i)=((3-2i)(1-4i))/((1+4i)(1-4i))=(3\cdot1-3\cdot4i-2i\cdot1-2i\cdot(-4i))/(1^2-(4i)^2)\\\\\\=(3-12i-2i+8i^2)/(1-16i^2)=(3-14i-8)/(1+16)=\boxed{-(5)/(17)-(14)/(17)i}`