Summary - Powers of i and patterns

Powers of i and Patterns

In this section, we will discuss the powers of i and the
patterns they create.

Powers of i
i^1 = i i^2 = -1 i^3 = -i i^4 = 1

Notice that the powers of i repeat every four powers.
This means that i^5 = i, i^6 = -1, and so on.

Patterns
The powers of i create a pattern that repeats every four
powers:

i, -1, -i, 1, i, -1, -i, 1, ...

This pattern is called the unit cycle and represents the
repeating nature of the complex number system.

Addition and Subtraction of Complex
Numbers
To add or subtract complex numbers, you simply add or
subtract the real parts and the imaginary parts
separately.

For example, consider the complex numbers a = 2 + 3i
and b = -1 + 4i. The sum of these complex numbers is:

a + b = (2 + (-1)) + (3 + 4)i = 1 + 7i

Additive Inverse in Complex Numbers
The additive inverse of a complex number is its
negation, or the number obtained by changing the sign
of each of its parts.

For example, the additive inverse of 2 + 3i is -2 - 3i.