For z = 2 + 3i, verify the following: \(\overline{z(\bar z)}\) = |z|

1.	For z = 2 + 3i, verify the following: \(\overline{z(\bar z)}\) = \|z\|2
Answer» z \(\bar z\)= (2 + 3i) (2 – 3i) = 4 – 9i² = 4 – 9(-1) …..[∵ i = -1] = 13 \|z\|² = \((\sqrt{2^2+3^2})^2\) = 2² + 3² = 4 + 9 = 13 \(\overline{z\bar z}\) = \|z\|²

For z = 2 + 3i, verify the following: \(\overline{z(\bar z)}\) = |z|2

Answer»

z \(\bar z\)= (2 + 3i) (2 – 3i)

= 4 – 9i²

= 4 – 9(-1) …..[∵ i = -1]

= 13

|z|² = \((\sqrt{2^2+3^2})^2\)

= 2² + 3²

= 4 + 9

= 13
\(\overline{z\bar z}\) = |z|²