Algebra 3/4 delves into advanced algebraic concepts, including polynomial functions, rational expressions, and complex numbers.
Complex numbers extend our number system to include solutions to equations like \( x^2 + 1 = 0 \). They are in the form:
\[ a + bi \]
where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit with the property \( i^2 = -1 \).
Complex numbers can be shown on a plane: the horizontal axis is the real part, and the vertical axis is the imaginary part.
They're essential for solving certain equations and show up in electronics, engineering, and physics.
\( 3 + 4i \) is a complex number where the real part is 3 and the imaginary part is 4.
Multiplying \( (2 + 3i) \) and \( (1 - i) \) gives \( 5 + i \).
Complex numbers combine real and imaginary parts to solve equations that real numbers alone can't.