Prove that z is real iff z=conjugate of z and z is imaginary iff z=- conjugate of z | Complex Number

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๐‘ง=๐‘งย ฬ… if and only if ๐‘ง๐œ–โ„ ๐‘ง=๐‘งย ฬ… if and only if ๐‘ง๐œ–โ„
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if `z-barz=0` then z is purely imaginary if `z-barz=0` then z is purely imaginary