7 - Polar and Rectangular Forms of Complex Numbers
The definition you've learned so far of a complex number of form
And, it makes total sense. The real part tells you where to go in the real axis and the imaginary part tells you where to go along the imaginary axis. This will form a sort of "rectangle".
The Polar Form
Much like this rectangle that can be used to express our vector representing this complex number, we can also represent this by a line starting from the origin, of a certain length, pointing at a certain angle.
Yup! As the radius of a circle!
The sine is what will give us the vertical component of this vector and the cosine gives us the horizontal component of this vector.
This allows us to effectively express a complex number
What is the r?
Simple, the radius of the circle! Otherwise, it's the magnitude of this "vector". The modulus/absolute value of the complex number.
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