# SHORTCUT TO FIND SQUARE ROOT OF COMPLEX NUMBER

Shortcut to Find Square Root of Complex Number :

Here we are going to see some example problems based on finding the square root of complex number.

## Shortcut to Find Square Root of Complex Number - Questions

Question 1 :

Find the square roots of (i) 4 + 3i

Solution :

Formula for finding square root of a complex number

Note :

If b is negative, b/|b| = −1, x and y have different signs.

If b is positive, b/|b| = 1, x and y have same sign.

|4 + 3i|  =  √42 + 32

=   √(16 + 9)

=   √25

=  5

By using the square root formula, we get

Here b is positive

√(4 + 3i)  =  ± ( √(5 + 4)/2 + i √(5 - 4)/2))

=  ± ( √(9/2) + i √(1/2))

=  ± (3 + i)/2

|4 + 3i|  =  √42 + 32

=   √(16 + 9)

=   √25

=  5

(ii)  -6 + 8i

Solution :

|-6 + 8i|  =  √(-6)2 + 82

=   √(36 + 64)

=   √100

=  10

By using the square root formula, we get

Here b is positive

√(-6 + 8i)  =  ± ( √(10 - 6)/2 + i √(10 - (-6)/2))

=  ± ( √(4/2) + i √(16/2))

=  ± ( √2 + i √8)

=  ± ( √2 + i 2√2)

(iii)  -5 - 12i

Solution :

|-5 - 12i|  =  √(-5)2 + (-12)2

=   √(25 + 144)

=   √169

=  13

By using the square root formula, we get

Here b is negative

√(-5 - 12i)  =  ± ( √(13 - 5)/2 +-i √(13 - (-5)/2))

=  ± ( √(8/2) - i √(18/2))

=  ± ( √4 - i √9)

=  ± ( 2 - i3)

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