Multiplying and simplifying complex numbers
In this article we shall explore how to multiply complex numbers and simplifying powers of i.
Quick summary
- Rules for multiplying brackets in algebra also apply here.
- You can simplify powers of I, remember that;
therefore;
Simplifying
Here we shall simplify powers of I such as;
Multiplication of complex numbers
We can multiply complex numbers in the same way that we multiply algebra.
Example: Multiply (2 + 3i) by (4 + 5i)
Answer
We must multiply out the brackets the same way as we would in algebra;
Remember that; i² = -1
Notice above that we have added the real parts together separately and added the imaginary parts together separately.
Example; Workout; (7 – 4i)²
We will need to express the expression in the form a + bi as we did above. Use algebra rules to multiply out the brackets;
