# How do you simplify #7+4i div 2-3i#?

##### 1 Answer

Jan 12, 2016

#### Explanation:

Basically,

To simplify

Your denominator is

You need to extend the fraction with

# ( 7 + 4i ) / (2 - 3i) = (( 7 + 4i )* (2 + 3i)) / ((2 - 3i)*(2 + 3i)) = (14 + 8i + 21i + 12 i^2) / (2^2 - (3i)^2) = (14 + 29i + 12 i^2) / (4 - 9 i^2)#

... remember that

# = (14 - 12 + 29i ) / (4 + 9) = (2 + 29i) / 13 = 2/13 + 29/13 i#