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Square root of complex numbers, solution of complex equation is considered one the most difficult concept.
4 Questions around this concept.
If then a value of is:
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.
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