Find the square roots of each complex number.
a. 5 + 12i
b. 5 − 12i

ANSWER:

Square root of 5 + 12i is 3+2i or -3 – 2i and square root of 5 – 12i is 3 – 2i or -3 + 2i.

SOLUTION:

Given, we have to find square roots of 5 + 12i and 5 – 12i

a) 5 + 12i

Now, square root of 5 + 12i  

Suppose that a + bi is a square root of 5 + 12i.  

Equate real and imaginary parts:

Since a must be real, a = 3 or -3.  

This gives b = 2 or -2, respectively.  

Thus, we have two square roots: 3+2i or -3-2i.

b) 5 - 12i

Now, square root of 5 - 12i  

Suppose that a - bi is a square root of 5 - 12i.  

Equate real and imaginary parts:

This gives b = 2 or -2, respectively.  

Thus, we have two square roots: 3 - 2i or -3 + 2i.

Hence, square root of 5 + 12i is 3+2i or -3 – 2i and square root of 5 – 12i is 3 – 2i or -3 + 2i.

ian gonna lie that is way to much