If x - iy - -a - ibc - id- prove that x2 - y22 - a2 - b2c2 - d2-

x+ι y=√(a+ι b/c +ι d) #8230;..(i) Taking conjugate both sides x ι y =√(a ι b/c ι d) #160; #8230;.(ii) #160;Multiplying (i) and (ii) #160; ...

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Modulus of a Complex Number

If x + iy =...

Question

If $x + i y = \sqrt{\frac{a + i b}{c + i d}}$ , prove that $(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}$ .

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Solution

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x - i y = \sqrt{\frac{a - i b}{c - i d}}

{(x^{2} + y^{2})}^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

(x + i y) = \sqrt{\frac{a + i b}{c + i d}}

(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}

If $x - i y = \sqrt{\frac{a - i d}{c - i d}},$ prove that $(x^{2} + y^{2})^{2} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}}$ .

\frac{(a + i b)}{(c + i d)} = x + i y

\frac{a - i b}{c - i d} = x - i y

\frac{a^{2} + b^{2}}{c^{2} + d^{2}} = x^{2} + y^{2}

I f x + i y = \sqrt{\frac{a + i b}{c + i d}}, t h e n (x^{2} + y^{2})^{2}

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