If (-7 - 24i)^{1/2} = x - iy,then x^2 + y^2 = | vedclass

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(B) Given that $\sqrt{-7 - 24i} = x - iy$. Squaring both sides,we get $-7 - 24i = (x - iy)^2 = x^2 - y^2 - 2xyi$. Equating the real and imaginary part

Vedclass · Accepted Answer

$25$

Vedclass · Answer

(B) Given that $\sqrt{-7 - 24i} = x - iy$. Squaring both sides,we get $-7 - 24i = (x - iy)^2 = x^2 - y^2 - 2xyi$. Equating the real and imaginary parts,we have $x^2 - y^2 = -7$ and $2xy = 24$. We know that $(x^2 + y^2)^2 = (x^2 - y^2)^2 + (2xy)^2$. Substituting the values,$(x^2 + y^2)^2 = (-7)^2 + (24)^2 = 49 + 576 = 625$. Taking the square root,$x^2 + y^2 = \sqrt{625} = 25$ (since $x^2 + y^2$ must be positive).

If $(-7 - 24i)^{1/2} = x - iy$,then $x^2 + y^2 = $

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