Addition and Subtraction of Complex Numbers

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