Difference between revisions of "Manuals/calci/IMEXP"

Revision as of 00:42, 24 April 2014

IMEXP(ComplexNumber)

$ComplexNumber$ is of the form a+bi.

Description

This function gives the exponential of a complex number.
In $IMEXP(ComplexNumber)$ , $ComplexNumber$ is of the form $x+iy$ , $x$ & $y$ 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 $e^{1}$ .
Let z be the Complex Number.Then the exponential of a complex number is : $IMEXP(z)=e^{z}=e^{x+iy}=e^{x}.e^{iy}=e^{x}.(cosy+isiny)=e^{x}.cosy+ie^{x}.siny$ .
Here Sin and Cos are trignometric functions. y is angle value in radians.
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'.
The Complex exponential function is denoted by "cis(x)"(Cosine plus iSine)
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 and IMEXP("0i") = 1

ZOS Section

The syntax is to calculate IMEXP in ZOS is .
- $ComplexNumber$ is of the form a+bi.
For e.g.,

References

Exponential function

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''IMEXP(z)'''</div><br/>
+<div style="font-size:30px">'''IMEXP(ComplexNumber)'''</div><br/>
-*where <math>z</math> is the complex number.
+*<math>ComplexNumber</math> is of the form a+bi.
 ==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(ComplexNumber)</math>, <math>ComplexNumber</math> is  of the form  <math>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.
-*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>.
+*Let z be the Complex Number.Then 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>.
+*Here Sin and Cos are trignometric functions. y is angle value in radians.
 *When  imaginary part is '0', it will give the exponent value of the real number. i.e <math>IMEXP(z) = EXP(z)</math> when imaginary number <math>iy</math> is '0'.
-*We can use COMPLEX function to convert the real and imaginary coefficients to a complex number.
+*The Complex exponential function is denoted by "'''cis(x)'''"(Cosine plus iSine)
+*We can use [[Manuals/calci/COMPLEX  | 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
@@ Line 15: / Line 21: @@
 #=IMEXP("2i") = -0.416146836547142+0.909297426825682i
 #=IMEXP("0") = 1 and IMEXP("0i") = 1
+==ZOS Section==
+*The syntax is to calculate IMEXP in ZOS is <math>IMEXP(ComplexNumber)</math>.
+**<math>ComplexNumber</math> is of the form a+bi.
+*For e.g.,
 ==See Also==

Difference between revisions of "Manuals/calci/IMEXP"

Revision as of 00:42, 24 April 2014

Contents

Description

Examples

ZOS Section

See Also

References

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