Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).
The process for solving complex number equations is similar to solving equations with real numbers. You first combine like terms and then isolate the variable on one side of the equation. However, when solving for complex numbers, you must also use the fact that i² = -1 to simplify the equation.
Yes, complex number equations can have multiple solutions. In fact, the fundamental theorem of algebra states that a polynomial of degree n will have n complex solutions, including any repeated solutions.
To graph complex numbers, you can use a coordinate plane with the real numbers on the x-axis and the imaginary numbers on the y-axis. For a complex number a + bi, you would plot the point (a, b) on the coordinate plane.
Complex numbers have many applications in fields such as physics, engineering, and economics. They are used to represent alternating currents, analyze electrical circuits, and model financial data. They are also used in signal processing, control systems, and quantum mechanics.