what is the square root of i, if i=x+yi?
what is the square root of 1-i? i'm getting problems like these in which╩I do╩not understand.
Thank You for your help, 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