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Complex Plane

Two complex n...

Question

Two complex numbers are given as,

$Z_{1}$ = $a_{1}$ + i $b_{1}$

$Z_{2}$ = $a_{2}$ + i $b_{2}$

For the complex numbers $Z_{1}$ and $Z_{2}$ to be equal, the necessary conditions are

Re ( Z₁) = Re( Z₂)

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Im( Z₁) = Im (Z₂)

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Both a & b

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All a, b & c

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Solution

The correct option is D
All a, b & c

For complex number $Z_{1}$ = $a_{1}$ + i $b_{1}$ , $Z_{2}$ = $a_{2}$ + i $b_{2}$ to be equal, $a_{1}$ = $a_{2}$ and $b_{1}$ = $b_{2}$
Hence Re( $Z_{1}$ ) = Re ( $Z_{2}$ )
Im( $Z_{1}$ ) = Im $(Z_{2})$
Also $| Z_{1} |$ = $| Z_{2} |$ is a necessary condition.

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