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If |z(1)|=|z(2)|, "is it necesssary that...

If `|z_(1)|=|z_(2)|, "is it necesssary that "z_(1) = z_(2)`.

Text Solution

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Given that, `|z_(1)|=|z_(2)|`
Let `z_(1)=x_(1)+iy_(1)" and " z_(2)=x_(2) + iy_(2)`
`rarr |x_(1)+iy_(1)|=|x_(2)+iy_(2)|`
`rArr x_(1)^(2)+y_(1)^(2) =x_(2)^(2)+y_(2)^(2) `
`rArr x_(1)^(2)=x_(2)^(2) ,y_(1)^(2)=y_(2)^(2) `
`rArr x_(1)=pmx_(2) ,y_(1)=pmy_(2)`
`rArr z_(1)=x_(1)+iy orz_(1)=pmx_(2)pmiy_(2)`
Hence, it is not neccessary that `z_(1) = z_(2)`.
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