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Question
Prove the following properties:
Re(z) = `(z + bar(z))/2` and Im(z) = `(z - bar(z))/(2"i")`
Solution
Let z = x + iy
`bar(z)` = x – iy
`(z + bar(z))/2 = (x + "i"y + x - "i"y)/2`
= `(2x)/2`
= x
= Re(z)
Hence proved.
`(z - bar(x))/(2"i") = ((x + "i"y) - (x - "i"y))/(2"i")`
= `(x + "i"y - x + "i"y)/(2"i")`
= `(2"i"y)/(2"i")`
= y
= Im(z)
Hence proved.
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