# Complex Number Calculator – Scientific Calculator

This comprehensive complex number calculator, a fully developed 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).

A complex number calculator (aka imaginary number calculator) is a scientific calculator that is also capable of performing mathematical operations and function evaluations with imaginary numbers, and in general, complex numbers.

In addition to performing the four basic operations of addition, subtraction, multiplication and division of complex numbers, this complex number calculator can be used to calculate powers and principal roots of complex numbers.

As a powerful scientific complex number calculator it can also be used to calculate exponential, logarithmic, trigonometric, hyperbolic, Γ (Gamma), ψ (psi) and ζ (zeta) functions with imaginary or complex number as arguments.

Complex numbers can be entered in the rectangular (standard) form a + bi, where a and b are the real part and imaginary part, respectively.

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

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

For instance, this imaginary / complex number calculator easily computes mathematical expressions containing complex numbers from the simplest forms such as (1+2i)-(3-4i), to arbitrary complicated forms such as sin(1+2i) / ln(3+4i) + atan(1+3i) − 4∠(1.8), which contains non-algebraic functions and complex numbers in rectangular and polar forms.

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## Instruction

This complex number calculator can be used as a fully-fledged scientific calculator to evaluate mathematical expression containing real, imaginary, and in general, complex numbers in any form.

Any operation or function evaluation you can perform with real numbers, you can also do with complex numbers by using this scientific complex number calculator. Type in complex numbers, using 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.

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

This scientific complex number 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 also input numbers in scientific or engineering notations, e.g., 1E6 or 1.2E-12, where the exponent is an integer. For any non-integer exponent such as decimal numbers, complex numbers or numerical expressions, you have to use parentheses, i.e., 2E(2.3) or 1.2E(1+2i).

Note: The function E() is defined as E(x) = 10^x. So E(2) is 100, which is the same as 1E2 (and not E2, which must be preceded by a literal real number).

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.

Also by checking Convert complex number results to other forms this rectangular / polar converter displays the results in standard form a + bi and converts the result of expressions to the polar form and other modular forms using Euler's formula:

• polar (phasor, angular): r∠(θ)
• exponential: re
• cis: r(cos(θ)+ i sin(θ))
• cis (phasor, angular): rcis(θ)
• modular: r(a/r + b/r i) where, r = √(a2 + b2), module or length or absolute value of a + bi, and θ = arctan(b/a), argument or angle of a + bi.

Note: as the value of trigonometric functions depend on the angle mode chosen, by selecting RAD, DEG or GRD the complex number calculator, needless to say, displays the computed values correspondingly. Note that, because functions of complex numbers are defined using the trig functions via Euler's identity, eix = cos(x)+ i*sin(x), their values depend on the angle mode selected although they may look non-trigonometric. For example, the value e2 is the same regardless of the angle mode selected. But the value of ei depends on the angle mode although ei looks non-trigonometric.

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 massage, if any.