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Question
z1 = 1 + i, z2 = 2 − 3i. Verify the following :
`bar("z"_1 - "z"_2) = bar("z"_1) - bar("z"_2)`
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Solution
z1 = 1 + i, z2 = 2 − 3i
∴ `bar("z"_1)` = 1 − i, `bar("z"_2)` = 2 + 3i
z1 − z2 = (1 + i) − (2 − 3i)
= 1 + i − 2 + 3i
= − 1 + 4i
∴ `bar("z"_1 - "z"_2)` = − 1 − 4i
`bar("z"_1) - bar("z"_2)` = (1 − i) − (2 + 3i)
= 1 − i − 2 − 3i
= − 1 − 4i
∴ `bar("z"_1 - "z"_2) = bar("z"_1) - bar("z"_2)`
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