I am a Junior in High School and would like to confirm the answer to this question: 2-3i/4+5i = the square root of 41? This is what I am coming up with, but am not sure I am doing it correctly. The directions are to simplify and write in the from a+bi.

Thanks,

2 - 3i 2 - 3i 4 - 5i 8 - 10i - 12i + 15i^2 -7 - 22i
----- = ------ *------ = -------------------- = ----------- =
4 + 5i 4 + 5i 4 - 5i 16 - 25i^2 41

-7/41 - (22/41)i