what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in whichÊI doÊnot understand. Thank You for your help, Arlene Hi Arlene, Every complex number z can be written z = x + iy where x and y are real numbers and i is the imaginary number that satisfies i^{ 2} = 1. x is called the real part of z and y is the imiginary part of z. In particular Suppose that x and y are real numbers and x + iy is the square root of i, then Since x^{ 2}  y^{ 2} + 2ixy and i are the same complex number their real and imaginary parts are equal. That is From the second equation y = ^{1}/_{2x} and thus, by substituting into the first equation, Finding the square root of 1  i is similar. Suppose that Harley
