# Polar complex form waves

1. Feb 11, 2015

### desklamp2

1. The problem statement, all variables and given/known data
What is the amplitude and phase of the complex function?

f(t) = (1-2i)e^(iwt)

2. Relevant equations
None/unknown
Normal Polar Form = Real*e^imaginary
i = e^pi/2*i
3. The attempt at a solution

I am trying to bring this into a normal polar form to easily see the phase and amplitude.

I have got e^iwt - 2e^i(wt+pi/2)

But now I do not know how to combine these two expressions to make 1 wave?

2. Feb 11, 2015

### soarce

Try to rewrite $$1-2i$$ as $$A\exp(i B)$$

3. Mar 1, 2015

### orsanyuksek2013

1 - 2i = √5 [cos (11 ⋅ pi / 12) + i sin (11 ⋅ pi / 12)] = √5 e^[i(11 ⋅ pi / 12)]

f(t) = (1-2i) [e^(iwt)]

f(t) = √5 e^[i(11 ⋅ pi / 12)] [e^(iwt)]

f(t) = √5 e^i[11 ⋅ pi / 12 + wt]

f(t) = √5 [cos ((11 ⋅ pi / 12) + wt)] + i √5 [sin ((11 ⋅ pi / 12) + wt)]

Re[f(t)] = √5 [cos ((11 ⋅ pi / 12) + wt)]

Amplitude: √5

Phase: (11 ⋅ pi / 12) + wt

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Örsan Yüksek

Last edited: Mar 1, 2015