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1.1.5 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  by typing EscapeKeyiiEscapeKey (see Section 1.1.7). The form  is normally what is used in output. Note that an ordinary i means a variable named  , not  .

This gives the imaginary number result  .

In[1]:=  Sqrt[-4]

Out[1]=

This gives the ratio of two complex numbers.

In[2]:=  (4 + 3 I) / (2 - I)

Out[2]=

Here is the numerical value of a complex exponential.

In[3]:=  Exp[2 + 9 I] //N

Out[3]=

x + I y the complex number
Re[z] real part
Im[z] imaginary part
Conjugate[z] complex conjugate  or
Abs[z] absolute value
Arg[z] the argument  in

Complex number operations.


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