Square Root 8 + 7i and 3 + -7i

a = bi = <-- Enter a and bi piece
c = di = <-- Enter c and di piece (not needed for square root or absolute value or conjugate)

Evaluate the complex number square root: √8 + 7i

The square root of a complex number a + bi, is denoted as root1 = x + yi and root2 = -x - yi
To find x and y, we first calculate r:
r = √a2 + b2
r = √82 + 72
r = √64 + 49
r = √113
r = 10.

Calculate y:
y = √½(r-a)
y = √½(10. - 8)
y = √½(2.6)
y = √3
y = 2

Calculate x:
x =b
2y

x =7
2(2)

x =7
2.3

x = 3.6

With x and y identified, our 2 complex roots x + yi and -x - yi become:
Root 1 = 3.6 + 2i
Root 2 = -3.6 - 2i