Question

find the square root of 1-2√2i
Please solve this urgently
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Answer 1

Step-by-step explanation:

The square root of 1-2√2i is-

let, the square root of 1-2√2i is x+iy.

Now, x+iy=√(1-2√2i)

squaring both side-

=(x+iy)^2=1-2√2i

=x^2+y^2.i^2+2xyi=1-2√2i

=x^2-y^2+2xyi=1-2√2i

comparing the real And imaginary part-

x^2-y^2=1 & 2xy=-2√2

And, x^2+y^2=3

Now,2x^2=4

x=√2 & x=-√2 ,y=1 & y=-1

So, square root of 1-2√2i is (√2+i) & (-√2-i)