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Complex Numbers

You can enter complex numbers in Mathematica just by including the constant I, equal to . Make sure that you type a capital I.
If you are using notebooks, you can also enter I as ImaginaryI by typing Esc ii Esc (see "Mathematical Notation in Notebooks: Numerical Calculations"). The form ImaginaryI is normally what is used in output. Note that an ordinary i means a variable named i, not .
This gives the imaginary number result 2i.
In[1]:=
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Out[1]=
This gives the ratio of two complex numbers.
In[2]:=
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Out[2]=
Here is the numerical value of a complex exponential.
In[3]:=
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Out[3]=
x+I ythe complex number x+i y
Re[z]real part
Im[z]imaginary part
Conjugate[z]complex conjugate z* or
Abs[z]absolute value VerticalSeparatorzVerticalSeparator
Arg[z]the argument CurlyPhi in VerticalSeparatorzVerticalSeparatoreiCurlyPhi

Complex number operations.