Question

For z = 2 + 3i verify the following:
i) $(z+\bar{z})$ is real
ii) $z-\bar{z}=6i$

Answer 1

Solution:

We know that if

$z = 2 + 3i \\ \\ then \\ \\ \bar z = 2 - 3i$
and is known as complex conjugate of z.

i) $(z+\bar{z})$ is real:

$z+\bar{z}= 2 + 3i + 2 - 3i \\ \\ z + \bar z = 4 \\ \\ so \\ \\ z + \bar z = real$
ii) $z-\bar{z}=6i$
$z-\bar{z}= 2 + 3i - 2 + 3i \\ \\ z - \bar z = 6i \\ \\ so \\ \\ z - \bar z = imaginary$
Hope it helps you.