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Addition

Under what co...

Question

Under what condition is the sum of two complex numbers $x_{1} + i y_{1}$ and $x_{2} + i y_{2}$ is a purely imaginary number?

A

x_{1} + x_{2} = 0.

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B

y_{1} + y_{2} = 0.

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C

x_{1} + x_{2} = y_{1} + y_{2} .

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D

x_{1} = y_{1}, y_{2} = x_{2} .

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Solution

The correct option is A $x_{1} + x_{2} = 0.$
Sum of complex numbers $x_{1} + i y_{1}$ & $x_{2} + i y_{2}$
$= x_{1} + i y_{1} + x_{2} + i y_{2}$
$= x_{1} + x_{2} + i (y_{1} + y_{2})$ is purely imaginary when $x_{1} + x_{2} = 0$
Ans: B

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