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**Problem/Statement**

The complex vector, [tex]\hat{v}(t) = cos(\omega t)\hat{x} + sin(\omega t)\hat{y}[/tex] is the unit vector [tex]\hat{v}(t)[/tex] expressed in instantaneous form.

**Question**

What I am wondering is, why is there no imaginary component "j" in say the sin component for the equation above?

Can we express a general notation for complex vectors as,

[tex]\hat{v}(t) = [cos(\omega t) + sin(\omega t)]\hat{x}] + [cos(\omega t) + sin(\omega t)]\hat{y}] [/tex]? Shouldn't that be the notation for the instantaneous form also?

Thanks,

Jeff

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