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Find the complex number z if zbarz = 2 ...

Find the complex number z if ` zbarz = 2 and z + barz=2`

Text Solution

Verified by Experts

The correct Answer is:
`1+i` or `1-i`
Let z = x + iy
` zbarz =2 Rightarrow (x + iy) (x-iy) =2 Rightarrow x^(2) +y^(2) =2 …(i)`
Also ` z+ barz = x + iy + x + iy = 2x +2 Rightarrow x=1 ..(ii) `
By (i) and (ii)
`x =1` , ` y =+-1 `
Hence, `z = 1 +i` or `1-i`
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