Square Root -2 + 6i 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: √-2 + 6i

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 = √-22 + 62
r = √4 + 36
r = √40
r = 6.8

Calculate y:
y = √½(r-a)
y = √½(6.8 - -2)
y = √½(8.8)
y = √4.4
y = 2.6

Calculate x:
x =b
2y

x =6
2(2.6)

x =6
4.1

x = 3

With x and y identified, our 2 complex roots x + yi and -x - yi become:
Root 1 = 3 + 2.6i
Root 2 = -3 - 2.6i