How do complex numbers work?

A complex number is the sum of a real number and an imaginary number. Recall, when a positive real number is squared, the result is a positive real number and when a negative real number is squared, again, the result is a positive real number. Complex numbers are a combination of real and imaginary numbers.

How do engineers use complex numbers?

Engineering Applications of Complex Numbers Complex numbers are used by Electrical & Electronic Engineers to define the Alternating Current or AC concept of Impedance, and in Fourier analysis they are used in the processing of radio, telephone and video signals, see this page for more details.

What is Pierre de Fermat’s contributions to math?

He single-handedly founded modern number theory as well as made advancements in areas such as probability theory, infinitesimal calculus, analytic geometry, and optics. Some of his contributions include Fermat numbers and Fermat primes, Fermat’s principle, Fermat’s Little Theorem, and Fermat’s Last Theorem.

What is the power of complex numbers?

Powers of complex numbers are just special cases of products when the power is a positive whole number.

What are the uses of complex numbers?

Complex numbers are used in engineering, particularly in electronics. Real numbers are used to denote electrical resistance, imaginary numbers are used to denote reactance , and complex numbers are used to represent impedance.

What are the operations of complex numbers?

About operations on complex numbers. A complex numbers are of the form , a+bi where a is called the real part and bi is called the imaginary part. This text will show you how to perform four basic operations (Addition, Subtraction, Multiplication and Division): For addition, add up the real parts and add up the imaginary parts.

What are examples of complex numbers?

Some examples of complex numbers are 3 − i, ½ + 7i, and −6 − 2i. The two parts of a complex number cannot be combined. Even though the parts are joined by a plus sign, the addition cannot be performed. The expression must be left as an indicated sum.