Question

Simplify 9 divided by 3 minus 2i

Answers:

A.-27 minus 18i divided by 14

B. 9i divided by 2 plus 3i

C. 27 plus 18i divided by five

D. 27 plus 18i divided by 13

Answer 1

`(9)/(3-2i)=(9)/(3-2i)\cdot(3+2i)/(3+2i)=(9(3+2i))/((3-2i)(3+2i))\\\\\text{Use distributive property and}\ a^2-b^2=(a-b)(a+b)\\\\=((9)(3)+(9)(2i))/(3^2-(2i)^2)=(27+18i)/(9-4i^2)=(27+18i)/(9-4(-1))=(27+18i)/(9+4)\\\\=\boxed{(27+18i)/(13)}\to\boxed{D.}`