State True or False.
If $(a + i b) (c + i d) (e + i f) (g + i h) = x + i y$ , then the value of $(a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2}) = x^{2} + y^{2}$

True

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False

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Solution

The correct option is A True
We have,
$(a + i b) (c + i d) (e + i f) (g + i h) = x + i y$

So,
$| (a + i b) (c + i d) (e + i f) (g + i h) | = | x + i y |$

We know that
$| z_{1} z_{2} | = | z_{1} | | z_{2} |$

Therefore,
$| a + i b | \times | c + i d | \times | e + i f | \times | g + i h | = x + i y$

$\sqrt{(a^{2} + b^{2})} \times \sqrt{(c^{2} + d^{2})} \times \sqrt{(e^{2} + f^{2})} \times \sqrt{(g^{2} + h^{2})} = \sqrt{x^{2} + y^{2}}$

On squaring both sides, we get
$(a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2}) = x^{2} + y^{2}$

Hence, this is the answer.

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Similar questions

If (a+ib)(c +id)(e + if)(g + ih) = A + iB , then ( $a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2})$ =

(a + i b) (c + i d) (e + i f) (g + i h) = A + i B

(a^{2} + b^{2}) (c^{2} + d^{2}) (e^{2} + f^{2}) (g^{2} + h^{2}) = A^{2} + B^{2}

\sqrt{\frac{a + i b}{c + i d}}

(a + i b) (c + i d) = A + i B

(a^{2} + b^{2}) (c^{2} + d^{2}) = A^{2} + B^{2}

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

x^{2} + y^{2}

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