WELCOME TO THE SQUARE ROOTS OF 4i!

HERE'S HOW YOU FIND THEM:

(0+4i) has length (magnitude) 4 and an angle to the x-axis, or modulus, of 90 degrees;
so the root circle has radius 4^1/2 = 2,
the first root is at theta1 = 90/2 = 45 degrees,
and the remaining root is at theta = 45 + 360/2 = 225 degrees.