Square root of complex numbers - Practice Questions & MCQ

Let z = x + iy, is the complex number whose square root we have to find

Since the square root of complex number must be a complex number, 

Now squaring both sides

Now comparing real and imaginary part and finding the value of a and b in terms of x and y 

 if Im(z) > 0 otherwise there will be -ve sign between real and imaginary part of the square root of z.

Note:

1. Students do not need to remember this formula. But, they are required to know the procedure to find the square root of a complex number.

2. If a + ib is one of the square root of z, then other square root must be -(a+ib) 

Complex Equations

To find the solution of the complex equation we substitute z = x + iy and find the value of x and y by comparing real and imaginary parts of the equation obtained. z = x+iy is the required solution.