How to Use the Complex/Imaginary Number Calculator

Complex Calculator

You can use this Complex Calculator to calculate imaginary numbers and complex numbers in any form. Type in complex numbers, using i or j for the imaginary unit. You can also use thhis calculator as an Imaginary Number Calculator to find sin(i), √(i) for example.

If you use j it is recommended to select the relevant option provided (go to > Use j for imaginary unit. Doing so makes the calculator to display the results using j).

The Complex Number Calculator displays the result as you type. You can change this behaviour (go to and uncheck calculate as you type). The label of STO button changes to Calculate, pressing it evaluates the expression and also stores the expression which you can recall it by pressing RCL.

You can use * or × for multiplication of complex numbers and / or ÷ for division of complex numbers.

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 number or expressions, you must 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 the Complex Number to Polar Form Calculator displays the results in standard form a+bi and optionally converts the result of expressions to polar form and other forms using Euler's formula:

where, r = √(a2 + b2), module or length or absolute value of a + bi, and θ = arctan(b/a), argument of a + bi.

Note: as the value of trigonometric functions depends on the angle mode chosen, by selecting RAD, DEG or GRD the calculator, needless to say, displays the computed values correspondingly. Note that, because functions of complex numbers may be defined by using the trig functions via Euler's formula, 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.

By using this Imaginary Calculator you can conveniently calculate the values of all standard functions on the imaginary unit by pressing the relevant option from the pop-up menu at the bottom of the calculator.

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.