# Help with Phasors

#### Pramu

Joined Feb 29, 2012
1
Im having a little trouble with phasor multiplication at the moment;
Let v(t)=Vm cos (ωt+θ);
Phasor of this is taken as V=Vm exp(jθ)

in phasor notation, V^2 = Vm exp(jθ) * Vm exp(jθ) = Vm^2 exp(2jθ) => v(t)^2= Vm^2 * (cos 2ωt+2θ)

But from trignomatry, v(t)^2 = Vm^2 * cos^(ωt+θ)
Why am i getting two different answers? Where have i gone wrong. Please give me an answer. Thanx

#### t_n_k

Joined Mar 6, 2009
5,448
On reflection I don't think one can directly equate non-linear transformations between the time & frequency domains. Although it would be worth reviewing the means by which the computation of power in the two domains is consistently resolved.

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#### bretm

Joined Feb 6, 2012
152
Vm cos (ωt+θ)

is not equal to

Vm exp(jθ)

The first is strictly real-valued and the second is complex-valued. When you square each of them you'll get different results as well.

The first is a time-varying wave with frequency ω and phase θ. The second is just a single point in the complex plane at angle θ from the real axis and distance Vm from the origin.