If 1- ix -1- ix - a - ib- then a 2- b 2-A- -1B- 0C- none of theseD- 1

The correct option is D 1 1 ix/1+ix=a+ib Taking modulus on both the sides, we get : |1 ix/1+ix|+|a+ib| ⇒ √(1^2+x^2)/√(1+ix)=√(a^2+b^2) ⇒ √(a^2+b^2)=1 Squaring ...

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Byju's Answer

Standard XII

Mathematics

Modulus of a Complex Number

If 1- ix /1+ ...

Question

$If \frac{1 - i x}{1 + i x} = a + i b, then a^{2} + b^{2} =$

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none of these

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Solution

The correct option is A
1

$\frac{1 - i x}{1 + i x} = a + i b$

Taking modulus on both the sides, we get :

$∣ ∣ \frac{1 - i x}{1 + i x} ∣ ∣ + | a + i b | \Rightarrow \frac{\sqrt{1^{2} + x^{2}}}{\sqrt{1 + i x}} = \sqrt{a^{2} + b^{2}} \Rightarrow \sqrt{a^{2} + b^{2}} = 1$

Squaring both the sides, we get :

$a^{2} + b^{2} = 1$

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Similar questions

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[RPET 1990]

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If 1−ix1+ix=a+ib,then a2+b2=

The correct option is A 1 1−ix1+ix=a+ib Taking modulus on both the sides, we get : ∣∣1−ix1+ix∣∣+|a+ib|⇒ √12+x2√1+ix=√a2+b2⇒ √a2+b2=1 Squaring both the sides, we get : a2+b2=1

$If \frac{1 - i x}{1 + i x} = a + i b, then a^{2} + b^{2} =$