Complex numbers are numbers that have both a real part and an imaginary part. They are usually written in the form a + bi, where a and b are real numbers and i is the imaginary unit (i.e. the square root of -1).
Complex numbers can be added and subtracted in the same way as real numbers. You simply add or subtract the real parts and the imaginary parts separately.
Multiplication of complex numbers is done by using the FOIL method, just like for binomials. Division of complex numbers is done by multiplying the numerator and denominator by the complex conjugate of the denominator.
Complex numbers can be represented on a graph using the complex plane. The real part is plotted on the x-axis and the imaginary part is plotted on the y-axis. The point where the two axes intersect represents the complex number 0 + 0i.
Complex numbers are used in calculus to solve various problems involving curves and surfaces. They are also used in complex analysis, a branch of mathematics that deals with functions of a complex variable. Examples of applications include computing derivatives and integrals of complex functions, and solving problems in fluid mechanics and electromagnetism.