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Question
For z = 2 + 3i verify the following:
`"z"bar("z")` = |z|2
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Solution
z = 2 + 3i
∴ `bar("z")` = 2 – 3i
and |z| = `sqrt(2^2 + 3^2)`
= `sqrt(4 + 9)`
= `sqrt(13)`
Also, `"z".bar("z") = (2 + 3"i").(2 - 3"i")`
= 4 – 9i2
= 4 + 9 ...[∵ i2 = – 1]
∴ `"z".bar("z")` = 13 = |z|2
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