Complex Number Calculator Online

The most comprehensive Online Complex Number Calculator that allows all operations with complex numbers and shows step-by-step work. Use this Complex Number Calculator as a Scientific Calculator. Type in any expression containing real numbers or complex numbers and get the calculated result in standard, polar, exponential and other forms. Instruction

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Number Notation — Format Result

Automatic (Default)
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Convert complex number results to other forms

With this Complex Number Calculator you can evaluate expressions of Complex Numbers from the simplest forms such as 1+2i+4, to arbitrary complicated forms such as sin(1+2i) / ln(3+4i) + exp(i)−4∠(1.8). Using Euler's formula the Complex Number Calculator converts standard form of the result to all forms such as polar, modular and exponential.

Click on to view error massage, if any.

Use this Online Complex Number Calculator the same way as you would use a scientific calculator. Type in complex numbers, using i as the imaginary unit. The complex number calculator displays the result as you type. 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 Online Complex Number Calculator displays the results in standard form a+bi and optionally converts the result of expressions containing complex numbers to the following forms using Euler's formula:

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