# Operations of Complex Numbers

Consider the following two complex numbers:

We can apply to them the following operations, as shown:

### Addition of Complex Numbers

The complex numbers must be in Cartesian form. We add the real parts together and the imaginary parts together.

### Subtraction of Complex Numbers

The complex numbers must be in Cartesian form. We subtract the real parts together and the imaginary parts together.

### Multiplication of Complex Numbers

In Cartesian form:

More useful is in the polar form:

### Division of Complex Numbers

In Cartesian form:

More useful is in the polar form:

### Powers of Complex Numbers

According to De Moivre's therem, the nth power of a complex number is:

### Roots of Complex Numbers

The nth root of a complex number is:

### Natural Logarithm of Complex Numbers

The natural logarithm of a complex number is:

Where k=0, 1, 2,… usually only used k=0.