How to convert wave from real to complex and vice versa? [closed]

1. How do you convert polar to complex?
2. How do you convert magnitude and phase to real and imaginary?
3. Why are we often using complex notation when dealing with waves?

How do you convert polar to complex?

It should be relatively easy to see that, if a complex number z has magnitude r and argument θ, then: z=r(cosθ+isinθ) This is called the polar form of a complex number. Thus, if you want to convert from polar form to rectangular form, remember that Re(z)=rcosθ and Im(z)=rsinθ.

How do you convert magnitude and phase to real and imaginary?

Conversion between the two notational forms involves simple trigonometry. To convert from polar to rectangular, find the real component by multiplying the polar magnitude by the cosine of the angle, and the imaginary component by multiplying the polar magnitude by the sine of the angle.

Why are we often using complex notation when dealing with waves?

The simple answer is that a wave has amplitude and phase, which requires two numbers. Complex numbers are one of the ways to represent a vector with magnitude and phase (rectangular coordinates).