Vector Addition - Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more.Presently, factorials of real negative numbers and imaginary numbers, except for zero and negative integers are interpolated using the Euler’s gamma function.Trigonometric Functions - Sine, cosine and tangent - the natural trigonometric functions.Triangle - Triangle analytical geometry.Roman Numerals - Roman numerals are a combinations of seven letters.Degrees - Radian is the SI unit of angle. Cartesian Coordinates - Convert between Cartesian and Polar coordinates. Values tabulated for numbers ranging 1 to 100. Numbers - Square, Cube, Square Root and Cubic Root Calculator - Calculate square, cube, square root and cubic root.Hyperbolic Functions - Exponential functions related to the hyperbola.Differential Calculus - Derivatives and differentiation expressions.Decimal System Prefixes - Prefix names used for multiples and submultiples units.Algebraic Expressions - Principal algebraic expressions formulas.AC - Active, Reactive and Apparent Power - Real, imaginary and apparent power in AC circuits.Mathematics - Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.Multiplying both the nominator and the denominator with the conjugate of the denominator is called rationalizing. Multiplying a complex number with its complex conjugate results in a real number likeĮxample - Multiplying a Complex Number with its Conjugateĭivision of complex numbers can be done with the help of the denominators conjugate: The complex conjugate of (a + jb) is (a - jb). Since j 2 = -1 - (8) can be transformed to = 0.52 + j 1.2 Multiplication of Complex Numbers = 4.38 - j 2.2 Subtracting Complex Numbers = 8 - j 2 Example - Adding Complex Numbers = ( r a cosθ a + r b cosθ b) + j ( r asin θ a + r b sin θ b) (6c) Example - Adding Complex Numbers = ( r a cosθ a + r b cosθ b) + j ( r asin θ a + r b sin θ b) (6b) Z a + Z b = r a (cosθ a + j sin θ a) + r b (cosθ b + j sin θ b) Z a = 3.606 e j 33.69 Adding or Subtraction of Complex Numbers Adding Complex Numbers The "argument" can be calculated by using eq. The "modulus" can be calculated by using eq. Example - Complex number on the Polar formĬan be expressed on the polar form by calculating the modulus and the argument. R can be determined using Pythagoras' theoremĪs we can se from (1), (3) and (6) - a complex number can be written in three different ways. Θ = argument (or amplitude) of Z - and is written as "arg Z" R = modulus (or magnitude) of Z - and is written as "mod Z" or |Z | Example - Adding two Complex numbersĪ complex number on the polar form can be expressed as
J b = imaginary part (it is common to use i instead of j)Ī complex number can be represented in a Cartesian axis diagram with an real and an imaginary axis - also called the Argand diagram:Įxample - Complex numbers on the Cartesian formĬan be represented in the Argand diagram:Īddition and Subtraction of Complex numbersĬomplex numbers are added/subtracted by adding/subtracting the separately the real parts and the imaginary parts of the number. There are two main forms of complex numbersĪ complex number consists of a real part and an imaginary part and can be expressed on the Cartesian form as
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