The mathematical symbol *i*, short for √(-1).

*i*

To enter a complex number:

*real-part*+*imag-part i*

Press 2nd *i* to paste *i*.

TI-83/84/+/SE/CSE/CE

1 byte

The *i* symbol is short for √(-1), and is used for complex numbers in algebra and complex analysis. On the calculator, entering *i* will not cause an error, even in Real mode, but operations that result in a complex number (such as taking the square root of a negative number) will. If you're dealing with complex numbers, then, it's best to switch to a+bi or re^θi mode.

# Advanced Uses

By using *i* in a calculation, the calculator switches to complex number mode to do it, even if in Real mode. So √(-1) will throw an ERR:NONREAL ANS, but √(0*i*-1) will not (even though it's the same number). This can be used to force calculations to be done using complex numbers regardless of the mode setting — usually by adding or subtracting 0*i*, although more clever ways can be found.

A good example of this technique is our Quadratic Formula routine.

# Related Commands

# See Also

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