Operations with Complex Numbers
A complex number is of the form a + bi , where a is called the real part and bi is called the imaginary part. When performing operations involving complex numbers, we will be able to use many of the techniques we used with polynomials.
Addition and Subtraction of Complex Numbers
When adding and subtracting complex numbers, we are only allowed to add real parts to other real parts, and imaginary parts to other imaginary parts.
Addition of two complex numbers a + b i and c + d i is defined as follows:
(a + b i) + (c + d i) = (a + c) + (b + d) i
The subtraction of two complex numbers a + b i and c + d i is defined as follows:
(a + b i) - (c + d i) = (a - c) + (b - d) i
Multiplication of Complex Numbers
Multiplying complex numbers works like multiplying two binomials.
The multiplication of two complex numbers a + b i and c + d i is defined as follows.
(a + b i)(c + d i) = (a c - b d) + (a d + bc) i
Division of Complex Numbers
We use the multiplication property of a complex number and its conjugate to divide two complex numbers.
Find out more about operations with complex numbers by reading the explanation below.
Operations with Complex Numbers
Practice: Answer the following exercises about operations with complex numbers.