Mathematica uses the capital letter I to represent the square root of -1. Type

and you'll get the answerSqrt[-1]

IYou can use I in expressions: the complex number 2 + 3i is represented as

in Mathematica. The generic complex number (x + y i) is written as2 + 3 I

or, equivalently,x + y I

Mathematica has a tendency to "alphabetize" things, so it will usually print out (x + y i) in the second form.x + I y

Mathematica uses the function **Conjugate**
to take the complex conjugate of a number.
Try it:

We know that the complex conjugate of (x + y i) is (x - y i). But Mathematica gives usa = 2 + 3 IConjugate[a]2 - 3 I

which, needless to say, is not very informative.Conjugate[x + y I]Conjugate[x + I y]

The problem is that we have not specified whether
x and y are real or complex numbers, and Mathematica
won't make any assumptions about x and y without
our help. If x and y are themselves complex
numbers, then the conjugate of (x + y i) is not
simply (x - i y). To tell Mathematica that x and
y are real numbers, use the **ComplexExpand**
command:

Now we get the expected result. Remember to useComplexExpand[ Conjugate[x + y I] ]x - I y

Other parts of the Mathematica tutorial:

- Mathematica's user interface
- Simple calculations
- Plotting lists of points
- Plotting functions
- Combining two or more plots
- Fitting data to polynomials
- Generating and manipulating lists of numbers
- Derivatives and integrals
- Special functions
- Contour and surface plots