Difference between revisions of "Manuals/calci/IMEXP"
Jump to navigation
Jump to search
Line 3: | Line 3: | ||
==Description== | ==Description== | ||
*This function gives the exponential of a complex number. | *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^ | + | *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'. | *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. | *We can use COMPLEX function to convert the real and imaginary coefficients to a complex number. |
Revision as of 06:00, 25 November 2013
IMEXP(z)
- where is the complex number.
Description
- This function gives the exponential of a complex number.
- In , is the complex number of the form , & are real numbers & is the imaginary unit. .
- Euler's formula states that , for any real number and is the base of the natural logarithm.
- The approximate value of the constant e=2.718281828459045 and it is equal to . So the exponential of a complex number is : .
- 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