Algebra 3/4

Algebra 3/4 delves into advanced algebraic concepts, including polynomial functions, rational expressions, and complex numbers.

Advanced Topics

Operations with Complex Numbers

Adding and Subtracting

Combine the real parts, then the imaginary parts. Easy!

Multiplying Complex Numbers

Use the distributive property and remember \( i^2 = -1 \).

Dividing Complex Numbers

Multiply the numerator and denominator by the conjugate of the denominator to make the denominator real.

Application in Real Life

Complex number operations are used in signal processing, alternating current (AC) electricity, and more!

Example: AC Circuits

Engineers use complex numbers to analyze voltage and current, making sure our devices work safely and efficiently.

Examples

  • Adding \( (2 + 5i) + (3 - 2i) = 5 + 3i \).

  • Dividing \( \frac{1 + 2i}{3 - 4i} = \frac{(1 + 2i)(3 + 4i)}{(3 - 4i)(3 + 4i)} = \frac{11 + 10i}{25} \).

In a Nutshell

Learn to add, subtract, multiply, and divide with complex numbers.