By selecting the Show work checkbox, the real & imaginary number calculator provides step-by-step solutions.
The complex number calculator performs conversions between rectangular and polar forms internally. By selecting the Convert results to all forms checkbox, you can display the results in rectangular (standard), polar (phasor), and other modular forms.
Powerful Features for Calculation on Complex Numbers
This real and imaginary number calculator provides the following functionalities.
Basic Operations
Perform basic operations – addition, subtraction, multiplication, and division – on complex numbers.
Powers and Roots
Calculate powers and principalroots of complex numbers.
Advanced Mathematical Operations
Calculate expressions involving trigonometric, hyperbolic, exponential, and logarithmic functions that have real, imaginary, or complex numbers as arguments.
Special Function Evaluation
Evaluate functions like Γ(), ψ(), and ζ(), corresponding to the Gamma, psi, and zeta functions, respectively.
What are complex numbers? Complex numbers are ordered pairs of real numbers (a,b), where a is called the real part and b is called the imaginary part. Instead of denoting a complex number with an ordered pair, it is customary to combine the pairs with a plus sign and denote the resulting complex number as a+bi, where i has the property that i2 = -1. In other words, i = √-1. Because there is no real number with a negative square, i is called the imaginary unit. Imaginary numbers are complex numbers whose real parts are zero, such as bi.
Note: Both the real part and the imaginary part are real numbers. The imaginary part is so called because it is the coefficient of the imaginary unit i.
All the laws and rules, including the commutative, associative and distributive laws, which we use in conjunction with the real number system, are also applicable to the complex number system. This makes the basic binary operations of addition, subtraction, multiplication and division of complex numbers easy to do. This real and imaginary numbers calculator uses the following rules to perform the four basic operations.
