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Modulus of a Complex Number

If x + iy =1+...

Question

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

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Solution

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

Taking modulus on both the sides :

$| x + i y | = | (1 + i) (1 + 2 i) (1 + 3 i) | \Rightarrow \sqrt{x^{2} + y^{2}} = \sqrt{1^{2} + 1^{2}} \sqrt{1^{2} + 2^{2}} \sqrt{1^{2} + 3^{2}} \Rightarrow \sqrt{x^{2} + y^{2}} = \sqrt{2} \sqrt{5} \sqrt{10} \Rightarrow \sqrt{x^{2} + y^{2}} = \sqrt{100}$

Squaring both the sides,

$\Rightarrow x^{2} + y^{2} = 100$

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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}

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

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

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

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