Complex numbers are numbers that contain both a real and imaginary part. They are represented in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit.
Complex numbers are important because they allow us to work with and solve problems that involve imaginary and complex quantities. They have numerous applications in fields such as physics, engineering, and mathematics.
To add or subtract complex numbers, simply combine the real parts and the imaginary parts separately. To multiply complex numbers, use the FOIL method, and to divide complex numbers, multiply by the complex conjugate of the denominator.
Complex numbers can be represented as points on a two-dimensional plane, known as the complex plane. The real part of the number is represented on the x-axis, and the imaginary part is represented on the y-axis. This allows for a visual representation of complex numbers and their operations.
A real solution to a problem is a solution that can be represented by a single value on the real number line. A complex solution involves imaginary and real components and cannot be represented by a single value on the real number line.