(A) Given,$(a+ib)^2=(c+id)^2(x+iy)$ Taking the modulus on both sides,we get: $|a+ib|^2 = |c+id|^2 |x+iy|$ Since $|z|^2 = a^2+b^2$ for $z = a+ib$,we ha

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(A) Given,$(a+ib)^2=(c+id)^2(x+iy)$ Taking the modulus on both sides,we get: $|a+ib|^2 = |c+id|^2 |x+iy|$ Since $|z|^2 = a^2+b^2$ for $z = a+ib$,we have: $a^2+b^2 = (c^2+d^2) \sqrt{x^2+y^2}$ Substituting the given values $a^2+b^2=4$ and $c^2+d^2=2$: $4 = 2 \sqrt{x^2+y^2}$ $\sqrt{x^2+y^2} = 2$ Squaring both sides,we get: $x^2+y^2 = 4$

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Mix Examples-Complex numbers

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If $a, b, c$ and $d \in \mathbb{R}$ such that $a^2+b^2=4$ and $c^2+d^2=2$ and if $(a+ib)^2=(c+id)^2(x+iy)$,then $x^2+y^2$ is equal to

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$1$

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If $a, b, c$ and $d \in \mathbb{R}$ such that $a^2+b^2=4$ and $c^2+d^2=2$ and if $(a+ib)^2=(c+id)^2(x+iy)$,then $x^2+y^2$ is equal to

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