Condition for Collinearity

Since , and are collinear and lie on a line passing through the origin, their arguments must be the same (if they are on the same side of the origin) or differ by . This means and have the same phase direction:

where and .

Product of Magnitudes

We are given the condition . In terms of complex numbers, this is:

While this matches option , it is a necessary but not sufficient condition because it ignores the fact that they are collinear. We need a relation that incorporates their shared direction.

Simplify the Relation

Substitute and into the product :

Given , we get:

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