How to Do Complex Numbers on the TI-84 Evo

By default, the TI-84 Evo returns ERROR: NONREAL ANSWER for the square root of a negative number. Switching one MODE setting, a+bi, fixes that and turns on full complex-number support.

Switch to a+bi mode

Ask for the square root of -1 in the calculator's default REAL mode and it stops with the error instead of an answer.

The TI-84 Evo showing ERROR: NONREAL ANSWER after taking the square root of -1 in REAL mode
  1. Press mode and arrow down to the row that reads REAL a+bi re^(θi). The dark bar at the top names it NUMBER TYPE: REAL/COMPLEX.
    The TI-84 Evo mode menu with the cursor on the REAL, a+bi, re to the theta i row
  2. Arrow right to a+bi and press enter. The status bar in the top-left switches from REAL to a+bi.
    The TI-84 Evo mode menu with a+bi selected and the status bar now reading a+bi
  3. Press clear to return to the home screen, then try the square root of -1 again. This time it returns i.
    The TI-84 Evo in a+bi mode showing the square root of -1 equal to i

Type i and do complex arithmetic

The imaginary unit i is the second function of the decimal point key, along the bottom row, so you reach it by pressing 2nd first:

TI-84 Evo keyboard with the decimal point key highlighted and i printed in blue above it
  1. Enter a complex expression. For (3+4i)+(1-2i), press ( 3 + 4, then 2nd and the decimal key to get i, then ). Build the second number the same way after a +.
  2. Press enter. The calculator adds the real parts and the imaginary parts separately and returns 4+2i.
    The TI-84 Evo home screen showing (3+4i)+(1-2i) evaluated to 4+2i

It multiplies complex numbers too, applying i2 = -1 on its own: (3+4i)(1-2i) comes back as 11-2i.

The TI-84 Evo showing (3+4i) times (1-2i) evaluated to 11-2i

Arithmetic with an i you typed yourself actually works even back in REAL mode. The a+bi setting matters when the calculator has to come up with the imaginary part on its own, like those square roots of negatives.

Good to know

  • The MATH menu has a CMPLX tab of complex-number tools. Press math and arrow right to CMPLX. You get conj( for the conjugate, abs( for the magnitude, plus real(, imag(, and angle(. For example, conj(3+4i) is 3-4i and abs(3+4i) is 5.
    The TI-84 Evo MATH menu open on the CMPLX tab showing conj, real, imag, angle, and abs
  • Wrap the numerator and denominator when you divide. Type (3+4i)/(1-2i), not 3+4i/1-2i. Without the parentheses the calculator reads it as 3 + (4i/1) - 2i and returns 3+2i, while the real quotient is -1+2i. Both are on the screen below for comparison.
    The TI-84 Evo showing 3+4i/1-2i evaluated as 3+2i and (3+4i)/(1-2i) evaluated as -1+2i
  • Resetting the calculator turns a+bi back to REAL. If square roots of negatives start erroring again after a reset, that is where to switch a+bi back on.