Question

The conjugate of complex no $\frac{1}{1+i}$ is ______.

• A. (1 + i)/ 2
• B. i/2
• C. (1 - i)/ 2
• D. (1 + 2i)/ 2

Answer 1

The correct option is A

(1 + i)/ 2

To get the conjugate of any complex number of a + ib form, change the sign of imaginary part of complex number.

If there is any imaginary part in the denominator, rationalize the given complex number and eliminate the imaginary part from denominator.

Let z = $\frac{1}{1+i}$

Rationalize the given complex number by multiplying 1 - i to numerator and denominator

z = $\frac{1}{1+i}$ $\times$ $\frac{1-i}{1-i}$

= $\frac{1-i}{1-i^2}$ = $\frac{1-i}{1-(-1)}$ = $\frac{1}{2}$(1 - i)

So, z = $\frac{1}{2}$(1 + i)