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Properties of Modulus

If | a + ib /...

Question

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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Solution

Taking modulus on both sides,

| $\frac{a + i b}{c + i d}$ | = |4+3i|

| $\frac{a + i b}{c + i d}$ | = $\sqrt{16 + 9}$

$\frac{\sqrt{a^{2} + b^{2}}}{\sqrt{c^{2} + d^{2}}}$ = $\sqrt{(} 25)$

Squaring on both sides,

| $\frac{a^{2} + b^{2}}{c^{2} + d^{2}}$ | = 25

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Similar questions

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

\frac{a^{2} + b^{2}}{c^{2} + d^{2}}

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

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

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