Numeric complex examples

Conversion between Cartesian and polar forms

Example #1

E^(I π/2)

Example #2

E^(I π)

Example #3

E^(-I π/2)

Example #4

z  = Sqrt[2] E^(I 3 π/4)

z  //  ComplexExpand

Example #5

z = 0 + 2  I;
{Abs[z],  Arg[z]}

Example #6

z = -1 + I;
{Abs[z],  Arg[z]}

Example #7

z = -3 - 4  I;
{Abs[z],  Arg[z]}  //  N

Algebraic operations

Example #1

I^3

Example #2

z  = 
      3  E^(I 2  π/3)  - 4  E^(-I π/6)

z  //  ComplexExpand

z  //  N

Example #3

z = (Sqrt[2]  -  2 I)^8

z  //  ComplexExpand

z  //  N

Example #4

z  =  (Sqrt[2] - 2  I)^-1

z  //  N

Example #5

Im[I E^(-I π/3)]

Examples #6

z1 = -4 + 3  I

z2 = 1 - I

Conjugate[z1]

z2^2

z1 + Conjugate[z2]

I z2

z1*Conjugate[z1]

E^z2  //  N

z1/z2