How to find Square root of a complex number
A number of the form where
Formula for finding square root of a complex number:
The square root of is
Proof. Let square root of
Equating real and imaginary parts we get
Solving (i) and (iii) we get
Similarly . Since 2ab=y , it is clear that both
Example : Find the square root of (-5-12i) .
Applying the formula for square root we get
Trick to find the square root of a complex number:
To find , follow the following steps:
- First find the number .
- Now factorise the given number in such a way that difference of square of these factors is equal to the real number .
Ex. Find the square root of 7+4i.
Sol. Find the number
12= 4×3 and
Ex. Find the square root of
Sol. Here and
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