Definition
- the complex numbers are combinations of both real parts and imaginary parts, denoted i.
- These can be written a+bi, where a and b are real numbers.
Some Operations
- $ j^2 = -1 $
- $ |a+bj| =\sqrt{a^2+b^2} $
- $ |z| = |\overline z| $ , where z is complex number
- Euler Equation : $ e^{aj} = cos a + isin a $
Examples
- $ |1+2j| = \sqrt{1^2+2^2} $
- $ |1+2j| = \sqrt{5} $
- $ |1-2j| = \sqrt{1^2+(-2)^2} =\sqrt{5} $
- $ e^{j60} = cos 60 + jsin 60 $
- $ e^{-j60} = cos 60 - jsin 60 $
