Difference between revisions of "Manuals/calci/IMEXP"

Revision as of 05:00, 25 November 2013

IMEXP(z)

where $z$ is the complex number.

Description

This function gives the exponential of a complex number.
In $IMEXP(z)$ , $z$ is the complex number of the form $z=x+iy$ , $x$ & $y$ are real numbers & $i$ is the imaginary unit. $i=sqrt{-1}$ .
Euler's formula states that $e^{ix}=cosx+isinx$ , for any real number $x$ and $e$ is the base of the natural logarithm.
The approximate value of the constant e=2.718281828459045 and it is equal to $e^{1}$ . So the exponential of a complex number is : $IMEXP(z)=e^{z}=e^{x+iy}=e^{x}.e^{iy}=e^{x}.(cosy+isiny)=e^{x}.cosy+ie^{x}.siny$ .
When imaginary part is '0', it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'.
We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

Examples

IMEXP("2+3i")=-7.315110094901102+1.0427436562359i
IMEXP("4-5i")=15.4874305606508+52.355491418482i
IMEXP("6")=403.428793492735
IMEXP("2i")=-0.416146836547142+0.909297426825682i
IMEXP("0")=1 andIMEXP("0i")=1

References

Exponential function

@@ Line 3: / Line 3: @@
 ==Description==
 *This function gives the exponential of a complex number.
-*In <math>IMEXP(z)</math>, <math>z<math> is the complex number of the form  <math>z=x+iy</math>, <math>x</math>&<math>y</math> are real numbers & <math>i</math> is the imaginary unit. <math>i=sqrt{-1}</math>.
+*In <math>IMEXP(z)</math>, <math>z</math> is the complex number of the form  <math>z=x+iy</math>, <math>x</math>&<math>y</math> are real numbers & <math>i</math> is the imaginary unit. <math>i=sqrt{-1}</math>.
-*Euler's formula states that <math>e^{ix}= cosx+isinx<math>, for any real number <math>x<math> and <math>e</math> is the base of the natural logarithm.
+*Euler's formula states that <math>e^{ix}= cosx+isinx</math>, for any real number <math>x</math> and <math>e</math> is the base of the natural logarithm.
-*The approximate  value of the constant e=2.718281828459045 and it is equal to <math>e^1</math>.                                                   So the exponential of a complex number is : <math>IMEXP(z)=e^z=e^(x+iy)=e^x.e^iy=e^x.(cosy+isiny)=e^x.cosy+ie^x.siny</math>.
+*The approximate  value of the constant e=2.718281828459045 and it is equal to <math>e^1</math>.                                                   So the exponential of a complex number is : <math>IMEXP(z) = e^z = e^{x+iy} = e^{x}.e^{iy} = e^{x}.(cosy+isiny)=e^x.cosy+ie^x.siny</math>.
 *When  imaginary part is '0', it will give the exponent value of the real number. *i.e.IMEXP(z)=EXP(z) when imaginary number (iy) is '0'.
 *We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.

Difference between revisions of "Manuals/calci/IMEXP"

Revision as of 05:00, 25 November 2013

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Description

Examples

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References

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