As part of a question I have to find the square root of -24 + 10i. I know that 1 + 5i is one square root, but I have no idea how to find this other than guess and check. I tried converting to polar form, but yet again it's the argument that's getting me. I know that x = -24, y = 10, and r = 26. But there doesn't seem to be a "nice" argument based on those values. arctan(10/-24) = 157.380... degrees, arccos(-24/26) = 157.380... degrees, and arcsin(10/26) = 157.380... degrees. So it's consistent, but it seems like there's no way it's going to give me an exact value for the square root, even though I know that there's a 'nice' root (1 + 5i). I thought about maybe just leaving the argument as (arccos(-24/26)) and then manipulating double angle identities, but I wasn't sure how to properly do this. Any help?