Advanced algebraic concepts including polynomials, rational expressions, and complex numbers.
Sometimes, equations don't have real-number solutions—like \( x^2 + 1 = 0 \). That's where complex numbers come in!
A complex number is written as \( a + bi \), where:
You can add, subtract, multiply, and even divide complex numbers. Just treat \( i \) like a variable, but remember \( i^2 = -1 \).
Complex numbers help solve equations that have no solutions in the real number system and are used in fields like engineering and physics.
You can plot complex numbers on a special graph called the complex plane, with the real part on the x-axis and the imaginary part on the y-axis.
\[i^2 = -1\]
Adding \( (2 + 3i) + (1 - 4i) = 3 - i \)
Multiplying \( (1 + i)(1 - i) = 1 - i^2 = 2 \)
Complex numbers extend the real numbers by including solutions to equations like \( x^2 + 1 = 0 \).