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<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==

==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(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>.                                                  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'.  

*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 [[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

#=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

==See Also==

==See Also==