Find the conjugate of \(\rm i + 3 \over 2i + 1\)

Question

Question

Answer 1

Concept:

Conjugate of a complex number:

For any complex number z = x + iy the conjugate z̅ is given by z̅ = x - iy

Calculation:

z = \(\rm i + 3 \over 2i + 1\)

z = \(\rm { i + 3 \over 2i + 1}\times {-2i+1\over-2i +1}\)

z = \(\rm -2i^2-6i+i+3\over1 - (2i)^2\)

z = \(\rm {5-5i\over1 + 4}\)

z = \(\rm {5(1 - i)\over5}\)

z = 1 - i

Conjugate of z = z̅ = 1 + i