This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# I

 Irepresents the imaginary unit .
• Numbers containing I are converted to the type Complex.
I can be entered as Esc ii Esc (for "imaginary i"):
Generate from square roots of negative real numbers:
Use I in exact and approximate calculations:
I can be entered as Esc ii Esc (for "imaginary i"):
 Out[1]=

Generate from square roots of negative real numbers:
 Out[1]=

Use I in exact and approximate calculations:
 Out[1]=
 Out[2]=
 Scope   (2)
Built-in mathematical functions work with complex numbers:
Extract imaginary parts:
Use Esc jj Esc to enter the engineering notation for I:
Use as a direction in infinite quantities:
Use as a direction in Limit:
Use as a generator of extension fields:
Factor integers over the Gaussians:
Use as an expansion point for series:
 Applications   (2)
Convert a complex number from polar to rectangular form:
Flow around a cylinder as the real part of a complex-valued function:
I is represented as a complex number with vanishing real part:
I is an exact number:
Use ComplexExpand to extract real and imaginary parts:
Use ExpToTrig to convert exponentials containing I into trigonometric form:
Simplify expressions containing I:
I is an algebraic number:
Trigonometric functions with purely imaginary arguments evaluate to simpler forms:
Obtain I in solutions of polynomial equations:
Roots of quadratic polynomials can evaluate to complex numbers:
Use Chop to remove small imaginary parts:
Use I as limits of integration:
Sort numbers by increasing imaginary parts:
Machine-precision evaluation of I yields an approximate zero real part:
Arbitrary-precision evaluation yields an exact zero real part:
Real and imaginary parts of complex numbers can have different precisions:
Arithmetic operations will typically mix them:
The overall precision of a complex number depends on both real and imaginary parts:
Complex numbers are atomic objects and do not explicitly contain I:
Disguised purely real quantities that contain I cannot be used in numerical comparisons:
Real roots of irreducible cubics still contain I in their algebraic forms:
Machine-precision numerical evaluation gives a spurious imaginary part:
Arbitrary-precision evaluation still leaves an imaginary part:
Use Reduce with an option to get explicitly real roots:
Finite imaginary quantities are absorbed by infinite real or complex quantities:
I cannot be used in intervals:
The symbol I needs to be evaluated to become a complex number:
Nested powers of I:
Find the limit in closed form:
Generate all possible nestings of powers of I:
Plot the points in the complex plane: