Complex Number Calculator Online

The best and most comprehensive Online Complex Number Calculator to evaluate any expression containing real, imaginary or complex numbers. Use this online complex number calculator as a scientific calculator to evaluate algebraic, trigonometric, logarithmic, hyperbolic, and in general, all types of functions with real, imaginary or complex number arguments. The complex number calculator optionally converts the results to polar (phasor), exponential and other modular forms using Euler's formula. Instruction

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With this Online 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).

Complex Numbers

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 negative square, i is called the imaginary unit.

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.

To do arithmetic/algebra with complex numbers, all the laws and rules, including the commutative, associative and distributive laws, which we use in conjunction with real number system, are also applicable to the complex number system. This makes the basic binary operations of addition, subtraction, multiplication and division easy to do.

Adding & Subtracting Complex Numbers

To add or subtract two complex numbers a+bi & c+di just add or subtract the corresponding real and imaginary parts of them. That is, (a+bi) + (c+di) = (a+c) + (b+d)i (a+bi) - (c+di) = (a-c) + (b-d)i

Multiplying Complex Numbers

To multiply two complex numbers a+bi & c+di use the the usual laws of algebra keeping in mind that i*i = -1. (a+bi)(c+di) = (ac - bd) + (ad + bc)i

Dividing Complex Numbers

To divide two complex numbers a+bi & c+di, first multiply by (c-di)/(c-di) and use the usual laws of algebra keeping in mind that i*i = -1. (a+bi)/(c+di) = (a+bi)(c-di)/(c2 + d2) = ((ac + bd) + (-ad + bc)i)/(c2 + d2)