Simplify $\dfrac{5+12i}{2-3i}$. Your answer should be of the form $a+bi$, where $a$ and $b$ are both real numbers and written as improper fractions (if necessary).

Guest Mar 27, 2018

#1**0 **

Simplify the following:

(12 i + 5)/(-3 i + 2)

Multiply numerator and denominator of (12 i + 5)/(-3 i + 2) by 2 + 3 i:

((12 i + 5) (3 i + 2))/((-3 i + 2) (3 i + 2))

(2 - 3 i) (2 + 3 i) = 2×2 + 2×3 i - 3 i×2 - 3 i×3 i = 4 + 6 i - 6 i + 9 = 13:

((12 i + 5) (3 i + 2))/13

(5 + 12 i) (2 + 3 i) = 5×2 + 5×3 i + 12 i×2 + 12 i×3 i = 10 + 15 i + 24 i - 36 = -26 + 39 i:

(39 i - 26)/13

Factor 13 out of 39 i - 26 giving 13 (3 i - 2):

(13 (3 i - 2))/13

(13 (3 i - 2))/13 = 13/13×(3 i - 2) = 3 i - 2:

** =3i - 2 OR -2 + 3i**

Guest Mar 28, 2018

edited by
Guest
Mar 28, 2018