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Question

POQis a straight line through the origin O,P and Q represent the complex numbers a+ib andc+id respectively and OP=OQ, then


A

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B

a+c=b+d

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C

arg(a+ib)=arg(c+id)

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D

None of these

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Solution

The correct option is B

a+c=b+d


(a,b) It is given that OP=OQ

|¯¯¯¯¯¯¯¯OP|=|¯¯¯¯¯¯¯¯¯OQ| |a+ib|=|c+id|

Also ¯¯¯¯¯¯¯¯OP =-¯¯¯¯¯¯¯¯¯OQ, ¯¯¯¯¯¯¯¯OP + ¯¯¯¯¯¯¯¯¯OQ=0

(a+c)+i(b+d) =0 a+c=0=b+d


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