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If sqrt(x+i y)=+-(a+i b), then findsqrt(...

If `sqrt(x+i y)=+-(a+i b),` then find`sqrt( x-i ydot)`

Text Solution

Verified by Experts

The correct Answer is:
`pm (b-ia)`
`sqrt(x+iy)=pm(a+bi)`
`or x + iy = a^(2)-b^(2) + 2iab`
`or x = a^(2)-b^(2), y = 2ab`
`therefore sqrt(-x-iy) = sqrt(-(a^(2)-b^(2))-2iab)`
`= sqrt(b^(2)+(ia)^(2) - 2iab)`
`= sqrt(b-ia)^(2)= pm(b-i)`
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