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

1.
When we divide two complex numbers, we multiply by the conjugate of the complex number in the denominator.

2. Remark: The conjugate of a+bi is a-bi.


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


`((3-2i)(1-4i))/((1+4i)(1-4i))= (3-4i-2i+(2i)(4i))/(1-(4i)^(2) ) = (3-6i-8)/(1+16)= (-5-6i)/(17)= (-5)/(17)- (6)/(17)i`