Complex Numbers and Imaginary Unit Quiz

Imaginary Unit

• The symbol i represents the imaginary unit.
• i is defined as the square root of -1.

Powers of i

• i² equals -1.
• i³ equals -i, indicating that as powers increase, the values cycle through.
• i⁴ equals 1, completing the cycle where every fourth power returns to 1.

Categories of Numbers

• Natural Numbers: All positive numbers excluding zero, starting from 1.
• Whole Numbers: Includes zero along with all positive numbers, starting from 0.
• Integers: Comprises all whole numbers and their negative counterparts, including negative numbers.
• Rational Numbers: Any number, decimal, or fraction that can be expressed as a fraction (e.g., 1/2, 0.75).
• Irrational Numbers: Numbers that cannot be expressed as fractions; they have non-repeating, non-terminating decimal expansions (e.g., √2, π).
• Real Numbers: Encompasses all numbers that can be found on the number line, excluding complex numbers.
• Complex Numbers: Composed of a real part and an imaginary part represented as a + bi, where a is real, and b is imaginary (e.g., 3 + 9i).

Additional Concepts

• Additive Inverse: The additive inverse of a number is its opposite, achieved by switching its sign; for example, the additive inverse of +5 is -5.