Difference between revisions of "Manuals/calci/IMEXP"
Jump to navigation
Jump to search
Line 1: | Line 1: | ||
− | <div style="font-size:30px">'''IMEXP( | + | <div style="font-size:30px">'''IMEXP(ComplexNumber)'''</div><br/> |
− | * | + | *<math>ComplexNumber</math> is of the form a+bi. |
+ | |||
==Description== | ==Description== | ||
+ | |||
*This function gives the exponential of a complex number. | *This function gives the exponential of a complex number. | ||
− | *In <math>IMEXP( | + | *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. | *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>. | + | *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'. | *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== | ==Examples== | ||
+ | |||
#=IMEXP("2+3i") = -7.315110094901102+1.0427436562359i | #=IMEXP("2+3i") = -7.315110094901102+1.0427436562359i | ||
#=IMEXP("4-5i") = 15.4874305606508+52.355491418482i | #=IMEXP("4-5i") = 15.4874305606508+52.355491418482i | ||
Line 15: | Line 21: | ||
#=IMEXP("2i") = -0.416146836547142+0.909297426825682i | #=IMEXP("2i") = -0.416146836547142+0.909297426825682i | ||
#=IMEXP("0") = 1 and IMEXP("0i") = 1 | #=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== | ==See Also== |
Revision as of 01:42, 24 April 2014
IMEXP(ComplexNumber)
- is of the form a+bi.
Description
- This function gives the exponential of a complex number.
- In , is 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 .
- Let z be the Complex Number.Then the exponential of a complex number is : .
- 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 when imaginary number 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 .
- is of the form a+bi.
- For e.g.,