JEE MATHEMATICS MCQ: COMPLEX NUMBERS

1 Easy

1 of 1

Application +4 | -1

Given,

z=f(x)+i g(x)

, where

i=\sqrt{-1}

and

f, g:(0,1) \rightarrow(0,1)

are real-valued functions, which of the following hold good?

View answer and explanation

Correct option: B

z=\frac{1}{1+i x}+i\left(\frac{1}{1-i x}\right)

Option B (

z=\frac{{1}}{{1+i x}}+i(\frac{{1}}{{1-i x}})

) is correct because it satisfies the condition that

f(x)

and

g(x)

are real-valued functions in the range (0,1) for

x \in (0,1)

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