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How to use complex numbers on a TI-84 Plus CE, TI-84 Plus or TI-83 Plus

By E-Code · updated

Press MODE, ▼ six times to the REAL a+bi row, ▶ onto a+bi and ENTER, then 2nd QUIT; now √(−4) gives 2i instead of an error. Type i with 2nd and . (the decimal point): (2+3i)(1−i) gives 5+i.

Step by step

  1. Open MODE. MODE Press MODE. The REAL a+bi row decides whether answers can be complex.
  2. Go down to the REAL row. ▼ ▼ ▼ ▼ ▼ ▼ Press ▼ six times to reach the REAL a+bi row.
  3. Move to a+bi. ▶ Press ▶ to move onto a+bi, complex numbers written as a + bi.
  4. Turn on a+bi. ENTER Press ENTER. a+bi is now highlighted.
  5. Go back home. 2nd MODE Press 2nd, then MODE (QUIT).
  6. Type √(−4). 2nd X² (-) 4 ) Press 2nd, then x² for √(, then (−), 4 and ).
  7. No more error. ENTER Press ENTER. In REAL mode this is an error; in a+bi mode the answer is 2i.
  8. Type (2+3i. ( 2 + 3 2nd . Type ( 2 + 3, then 2nd and . (the decimal point): i is written above it.
  9. Times (1−i). ) ( 1 − 2nd . ) Type ) ( 1 − i ): 2nd and . again for i.
  10. Multiply them. ENTER Press ENTER.
  11. Read the answer. (2 + 3i)(1 − i) = 5 + i. The calculator uses i² = −1 for you, and gives the answer as a + bi.

What the screen shows

(2 + 3i)(1 − i) = 5 + i. The calculator uses i² = −1 for you, and gives the answer as a + bi.

Look for 5+𝑖 on the screen.

Try it with the keys lit up

This guide is one of E-Code's Learn lessons. Open it on E-Code's TI-84 calculator and each key lights up in turn as you press it.

Try “Use complex numbers” on the TI-84 calculator

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