Complex numbers can be multiplied by constants, added and subtracted just like other types of numbers.

### Multiplying by a Constant

When a complex number is multiplied by a constant both the real and the imaginary parts are multiplied by the constant.

**Example**

3(4 + 5i) =12 + 15i

### Adding Complex Numbers

When two or more complex numbers are added, the real parts are added first followed by the imaginary parts. The answer is another complex number.

**Example**

If h = 3 + 4i and k = 4 + 5i, find h + k

h + k = (3 + 4i) + (4 + 5i) =7 + 9i

### Subtracting Complex Numbers

When two or more complex numbers are subtracted, the real parts are subtracted first followed by the imaginary parts. The answer is another complex number.

**Example**

If s = 5 + 3i and t = 1 − 7i, find s – t

s − t = (5 + 3i) – (1 − 7i) =4 + 10i