If - a - ib - c - id -4-3 i - then the value of - a 2- b 2- c 2- d 2- is

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Cube Root of a Complex Number

If | a + ib /...

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If | $\frac{a + i b}{c + i d}$ | = |4+3i| , then the value of | $\frac{a^{2} + b^{2}}{c^{2} + d^{2}}$ | is _________

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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}}

\frac{a + i b}{c + i d} = p + i q

\frac{a - i b}{c - i d} = p - i q

p^{2} + q^{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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