Question

Find the square roots of the complex number 3 - 4i​

Answer 1

Answer:

Let, √3+4i = √x +i√y

Then,

(√3+4i)²= (√x + i√y)²

=> 3+4i = x-y + 2i√xy

Comparing real part and imaginary part, we get

3= x-y and 2√xy = 4

xy = 4

• x-y= +5

( As x {not equal to} 5; √x is real part)

• x = 4, y = 1

=> √x = +2, √y = +1

Hence square root is ±(2+i)

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