RedCrab Math Tutorial


    Real numbers   Complex numbers   Sets  
Complex Numbers
A complex number z consists of a real part a and an imaginary part b. The imaginary part is marked with the letter i

z = a + b i

The imaginary number i has the property

i² = -1

The value of a complex number corresponds to the length of the vector z

The following figure shows a graphical representation of a complex number

Addition and subtraction of complex numbers
The addition and subtraction of complex numbers corresponds to the addition and subtraction of the vectors. The real and imaginary components are added or subtracted

z1 + z2 = x1 + x2 + i (y1+ y2)

z1 + z2 = x1 - x2 + i (y1- y2)

The following figure shows an addition and graphical display in the RedCrab Calculator
Multiplication of complex numbers
The multiplication is done by multiplying the parentheses.

z1 · z2 = (x1 + y1 i) · (x2 + y2 i)

= x1 · x2 - y1 · y2 + i (x1 · y2 + y1 · x2)

The following figure shows the multiplication and graphic display in the RedCrab Calculator
Elementary complex functions RedCrab Calculator
    Calculator Syntax

Complex number

z = x + y ·i z = x + yi

Real part

Re (z) = x Re (z)

Imaginary part

Im (z) = y Im (z)

Conjugate complex number 

z = x - y ·i Conjugate (z)


|z| = √x² + y² Magnitude (z)


1 / z
Eexponential function ez = ex · cos y + (ex sin y) · i ez




ln z= 1/2 ln (x² + y²) + atan (y / x) · i Ln (z)


sin z = sin x · cosh y + (cos x · sinh y · i) Sin (z)


con z = cos x · cosh y + (sin x · sinh y · i) Cos (z)

Sinus hyperbolic

sinh z = sinh x · cos y + (cosh x · sin y · i) Sinh (z)

Cosine hyperbolic

cosh z = cosh x · cos y - (sinh x · sin y · i) Cosh (z)


Tan (z)


External References  
  Products RedCrab Calculator RedCRab Manual  
      RedCrab Software - Singapore - Sengkang West Way

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