Final answer:
The square roots of a complex number 50 + 50i√3 are found by using the technique of equating to (x + yi)^2 and solving the resulting system of equations for x and y to identify the square roots in a + bi form.
Step-by-step explanation:
To find the square roots of a complex number in the form a + bi, we can use the technique of equating our number to (x + yi)^2, where x and y are the real and imaginary parts, respectively, of the square root we are trying to find. Squaring x + yi gives us x^2 - y^2 + 2xyi which can be set equal to our given complex number, 50 + 50i√3.
Setting the real parts equal, we get x^2 - y^2 = 50, and setting the imaginary parts equal gives us 2xy = 50√3. Solving these equations simultaneously will lead us to the values of x and y, which define our square roots.