Difference between revisions of "Manuals/calci/IMEXP"
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*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 | + | *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. | *We can use COMPLEX function to convert the real and imaginary coefficients to a complex number. | ||
Revision as of 06:13, 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 when imaginary number 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