1.

If z is a complex number, thenA. `|z^(2)|gt|z|`B. `|z^(2)| = |z^(2)|`C. `|z^(2)|lt|z|^(2)`D. `|z^(2)|ge|z|^(2)`

Answer» Correct Answer - B
If z is a complex number, then `z = x + iy `
`|z| = |x + iy| "and" |z|^(2) = |x +iy|^(2)`
`rArr |z|^(2) = x^(2) +y^(2)" "...(i)`
and ` z^(2) = (x + iy)^(2) = x^(2) + i^(2) y^(2) + i2xy`
`rArr |z^(2)|=sqrt((x^(2) - y^(2) )^(2) + (2xy)^(2))`
`rArr |z^(2)| = sqrt(x^(4) + y^(4) - 2x^(2)y^(2) + 4x^(2) y^(2))`
`rArr |z^(2)| = sqrt(x^(4) + y^(4) - 2x^(2)y^(2)) =sqrt((x^(2) +y^(2)))^(2)`
`rArr |z^(2)| = x^(2) + y^(2)`
From Eqs (i) and (ii),
`|z|^(2)=|z^(2)|`


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