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Let z and w be two nonzero complex numbe...

Let `z and w` be two nonzero complex numbers such that `|z|=|w| and arg(z)+a r g(w)=pidot` Then prove that `z=- barw dot`

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Verified by Experts

`arg(w) = theta.` Then `arg(z) = pi - theta`. Therefore ,
`w= |w| (cos theta + isin theta)`
`and z|z| (cos (pi - theta) + sin (pi- theta))`
`=|w| (-cos theta + I sin theta )" "[because|z| = |w|]`
`= -|w| (cos theta - isin theta) = - barw`.
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