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

$The imaginary numberihas the property$

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

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 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) Value |z| = √x² + y² Magnitude (z) Reciprocal 1 / z Eexponential function ez = ex · cos y + (ex sin y) · i ez Root √z Logarithm ln z= 1/2 ln (x² + y²) + atan (y / x) · i Ln (z) Sine sin z = sin x · cosh y + (cos x · sinh y · i) Sin (z) Cosine 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) Tangent Tan (z)

External References

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