Scientific Calculator: Compute with Real and Imaginary Numbers

This comprehensive scientific calculator is for evaluating mathematical expressions containing real, imaginary and, in general, complex numbers in any form including rectangular (standard) form a+bi and polar form r∠(θ).

This scientific calculator is capable of performing mathematical operations and function evaluations with complex numbers—both real and imaginary numbers.

You can enter complex numbers in the rectangular (standard) form a+bi, where a and b are the real part and imaginary part, respectively.

Comprehensive Scientific Calculator

Perform basic and advanced operations with full support for power (including exponential and root), logarithm, trigonometric, and hyperbolic functions using complex numbers as their arguments.

Complex numbers can also be entered in the polar form r∠ θ, where r is the signed modulus (or magnitude) and θ is the argument (or angle) of the complex number.

Furthermore, this calculator shows work step-by-step and converts the complex number results to standard, polar and other modular forms.

Number Format | Output
⚙
?
Results are show here
4

Instruction

Use +, -, * and / for the basic operations of addition, subtraction, multiplication and division. You can also use × for multiplication and ÷ for division.

You can also use ∥ for parallel sum (or reduced sum), a binary operation used in fields like electrical engineering.

This scientific calculator displays the result as you type. You can change this behaviour. Go to ⚙ and clear the Calculate as you type checkbox. The label of STO changes to Calculate, pressing it evaluates the expression and also stores the expression which you can recall it by pressing RCL.

You can use i or j for the imaginary unit. If you use j it is recommended to select the Use j for imaginary unit option (go to ⚙). Doing so makes the imaginary number calculator to display the results using j.

You can input numbers in scientific (or engineering) notation (e.g., 1E4 or 1.2E-6), where the exponent must be an integer. For non-integer exponents, you must use parentheses (e.g., 2E(2.3) or 1.2E(1+2i)).

Remark: Our scientific calculator introduces the function E() defined on complex numbers as E(z) = 10^z. Therefore, E(2) equals 100, which is the same as 1E2. It is important to note that, unlike E(2), the entity E2 (without parentheses) is invalid, as it must be preceded by a real literal number, e.g., 1E2.

The calculator optionally displays the result in Fixed, Scientific and Engineering notations. In default notation the calculator uses other notations to display the results of calculations depending on how big or small they are.

By checking Show work the calculator displays the intermediate calculations from start to end.

lso by checking Convert results to other forms Our scientific complex number calculator performs conversions and displays results in multiple forms, including:

Here, r is the magnitude (or modulus or length or absolute value) of the complex number, and θ denotes its argument (or phasor or angle).

Remark: Transcendental (non-algebraic) functions of complex numbers, such as the exponential and logarithm, are defined using the trigonometric functions via Euler's formula eiz = cos(z) + i*sin(z), their values depend on the angle mode selected, even though they might appear to be non-trigonometric. For example, the value e2 is the same regardless of the angle mode selected. However, the value of ei depends on the angle mode because it's equal to cos(1) + i*sin(1) (where z = 1).

For mobile devices you can suppress (default) or activate the pop-up keyboard by checking or un-checking the Prevent System keyboard from popping up option. This is tested on Android devices and may not currently work on iOS.

Click ❓ to view error message, if any.