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Modulus of a Complex Number

If 1-i 1-2...

Question

If $(1 - i) (1 - 2 i) (1 - 3 i) . . . (1 - n i) = x - i y$ , then $2 \cdot 5 \cdot 10..... (1 + n^{2}) =$

A

x^{2} + y^{2}

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B

x + y

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C

x^{2} - y^{2}

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D

x - y

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Solution

The correct option is A $x^{2} + y^{2}$
$(1 - i) (1 - 2 i) (1 - 3 i) . . . . . . . (1 - n i) = x - i y$

Taking modulus on both sides

$| (1 - i) (1 - 2 i) (1 - 3 i) . . . . . . . . (1 - n i) | = | x - i y |$

$\sqrt{2} \cdot \sqrt{5} \cdot 10 . . . . . . . . \sqrt{1 + n^{2}} = \sqrt{x^{2} + y^{2}}$

Squaring on both sides

$2 \cdot 5 \cdot 10.......... (1 + n^{2}) = x^{2} + y^{2}$

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Similar questions

(1 + i) (1 + 2 i) (1 + 3 i) . . . . (1 + n i) = x + i y

2.5.10....... (1 + n^{2}) = x^{2} + y^{2}

(1 + i) (1 + 2 i) (1 + 3 i) . . . . (1 + n i) = x + i y

2.5.10..... (1 + n^{2}) = x^{2} + y^{2}

$If x + i y = (1 + i) (1 + 2 i) (1 + 3 i), then x^{2} + y^{2}$

x + i y = (1 + i) (1 + 2 i) (1 + 3 i)

, then x² + y² =
(a) 0
(b) 1
(c) 100
(d) none of these

(1 - i) (1 + 2 i) (1 + 3 i) . . . . (1 + n i) = α + i β

2 \cdot 5 \cdot 10 . . . . (1 + n^{2}) =

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