If $x + i y = (a + i b) / (c + i d)$ , then $(x^{2} + y^{2})^{2} = (a^{2} + b^{2}) / (c^{2} + d^{2})$ . If this is true enter 1, else enter 0.

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Answer 1

$x + i y = (a + i b) / (c + i d)$
by taking modulus
$∣ x + i y ∣ = ∣ ∣ ∣ ∣ ∣ \frac{a + i b}{c + i d} ∣ ∣ ∣ ∣ ∣$
$x^{2} + y^{2} = \frac{a ^{2} + b ^{2}}{c ^{2} + d ^{2}}$
$\Rightarrow x^{2} + y^{2} = \frac{a ^{2} + b ^{2}}{c ^{2} + d ^{2}}$
$\Rightarrow (x^{2} + y^{2})^{2} = \frac{a ^{2} + b ^{2}}{c ^{2} + d ^{2}}$

Ans: 1

Answer 2

x + i y = (a + i b) / (c + i d)

by taking modulus

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

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

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

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

Ans: 1