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

Question

3-2i/1+4i

Answer 1

Multiply both numerator & denominator by the conjugate of the denominator. Use FOIL in each case, remembering, of course, that i² = -1. Piece of cake. This guarantees a Real final denominator.

Answer 2

Multiply the numerator and denominator by the conjugate of (1 + 4i), which is (1 - 4i)

 

( 3 - 2i)(1 - 4i)

(1 + 4i)(1 - 4i)

 

= 3 - 12i - 2i + 8i²

       1 - 16i²

 

= 3 - 14i - 8

     1 + 16

 

= -5 - 14i

      17

 

= -5/17 - 14i/17

 

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

 

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