Addition(a + bi) + (c + di) = (a + c) + i(b + d) 
Subtraction(a + bi)  (c + di) = (a  c) + i(b  d) 

Multiplication(r_{1}∠θ_{1})(r_{2}∠θ_{2}) = (r_{1}•r_{2)}∠(θ_{1} + θ_{2})(a + bi)(c+di) = (ac  bd) + i(ad + bc) 
Division

tan(a+bi) =  tan(a) + tanh(b)•i  =  sin(a)•cos(a) + i•sinh(b)•cosh(b) 
1  i•tan(a)•tanh(b)  cos^{2}(a) + cosh^{2}(b)  1 
cos^{1}(z) = i•ln(iz+√(1z^{2})) +  π 
2 
tan^{1}(z) =  i  (ln(1iz)  ln(1+iz)) 
2 
x  y  arg(x + yi) 

>0  ≠0  tan^{1}(y/x) 
>0  =0  0 
0  >0  90^{o} or π / 2 
0  <0  90^{o} or π / 2 
<0  >0  tan^{1}(y/x) + 180^{o} (or π) 
<0  <0  tan^{1}(y/x)  180^{o} (or π) 
<0  0  180^{o} (or π) 
0  0  does not exist 
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