Evaluate this complex number square root:
√8 + 7i
Define the complex square root:
√a + bi:
root1 = x + yi
root2 = -x - yi
Calculate r:
r = √a2 + b2
r = √82 + 72
r = √64 + 49
r = √113
r = 10.630145812735
Calculate y:
y = √½(r-a)
y = √½(10.630145812735 - 8)
y = √½(2.6301458127346)
y = √1.3150729063673
y = 1.1467662823642
Calculate x:
| x = | b |
| 2y |
| x = | 7 |
| 2(1.1467662823642) |
| x = | 7 |
| 2.2935325647283 |
x = 3.0520604362246
Final Answer
Root 1 = 3.0520604362246 + 1.1467662823642i
Root 2 = -3.0520604362246 - 1.1467662823642i
Root 2 = -3.0520604362246 - 1.1467662823642i
