represents the imaginary unit .
- Numbers containing I are converted to the type Complex.
- I can be entered in StandardForm and InputForm as , ii or \[ImaginaryI].
- , jj and \[ImaginaryJ] can also be used.
- In StandardForm and TraditionalForm, I is output as .
Examplesopen allclose all
Basic Examples (3)
Generalizations & Extensions (6)
Properties & Relations (12)
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:
Possible Issues (9)
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:
Wolfram Research (1988), I, Wolfram Language function, https://reference.wolfram.com/language/ref/I.html (updated 2002).
Wolfram Language. 1988. "I." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2002. https://reference.wolfram.com/language/ref/I.html.
Wolfram Language. (1988). I. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/I.html