Evaluate the expression and write your answer in the form a + bi.

3+2i
____
1-4i

i thought the answer was 11+(14i/16) but i was wrong :( any help is greatly appreciated.

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

rationalize by multiplying top and bottom by the denominator's conjugate: (1+4i):

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

[3(1) + 3(4i) +2i(1) +2i(4i)] / [1(1) + 1(4i) -4i(1) -4i(4i)]

[3 +12i +2i +8i^2] / [1 +4i -4i -16i^2]

[3 +14i +8i^2] / [1 -16i^2]

NOTE that i^2 = -1

[3 +14i +8(-1)] / [1 -16(-1)]

(3 +14i -8) / (1 +16)

(-5 +14i) / 17

aka

-5/17 + 14i/17

-5/17 + (14/17)i

Quite close actually.

Try multiplying the numerator and denominator by 1 + 4i.