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