PHY354H1 Lecture Notes - Bmw I8, Elementary Algebra, Cartesian Coordinate System
Document Summary
We will list the basic properties of complex numbers you need to know for the course: every complex number can be written in the form z = x + iy, where i2 = 1. The real part of z is x, and the imaginary part of z is y. We write re{z} = x and im{z} = y: example: show that. |z| = zz = x2 + y2: example: find the complex conjugate and magnitude of z = 11: the polar form of a complex number is related to polar coordinates in the cartesian plane. You can use taylor series expansion of sin , cos , and ei to prove de moivre"s theorem: cos + i sin = ei (5) This lets us write z in polar coordinates: z = x + iy. = (r cos ) + i(r sin )
