POQ is a straight line through the origin O. | vedclass

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(D) Given that $POQ$ is a straight line passing through the origin $O$,the points $P$,$O$,and $Q$ are collinear. Since $OP = OQ$ and they lie on a str

Vedclass · Accepted Answer

Both $A$ and $B$

Vedclass · Answer

(D) Given that $POQ$ is a straight line passing through the origin $O$,the points $P$,$O$,and $Q$ are collinear. Since $OP = OQ$ and they lie on a straight line through the origin,$P$ and $Q$ are reflections of each other with respect to the origin. Thus,the complex number $z_2 = -z_1$. $c + id = -(a + ib) = -a - ib$. Comparing real and imaginary parts,we get $c = -a$ and $d = -b$,which implies $a + c = 0$ and $b + d = 0$. Also,the magnitude condition $OP = OQ$ implies $|z_1| = |z_2|$,which means $|a + ib| = |c + id|$. Therefore,both conditions $A$ and $B$ are correct.

$POQ$ is a straight line through the origin $O$. $P$ and $Q$ represent the complex numbers $z_1 = a + ib$ and $z_2 = c + id$ respectively. If $OP = OQ$,then:

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