# How to Plug in Imaginary Numbers on a TI-84 Plus

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Imaginary numbers and complex numbers (numbers with both real and imaginary components) are common in mathematics and electrical engineering. While the TI-84 Plus will readily display imaginary numbers, it is less obvious how to enter imaginary numbers. It supports two methods of entering complex numbers: rectangular mode and polar mode. In rectangular mode, you will enter the number as the sum of a real part and a complex part. In polar mode, you will enter the number as a radius and an angle.

• Set the appropriate display mode by pressing "Mode," the down arrow six times and using the right and left arrows to highlight the appropriate mode and then "Enter" to select it. The "Real" mode restricts the display of numbers to real numbers. The "a + bi" format displays numbers in rectangular mode, and "re^Ti" displays complex numbers in polar form.

• Enter your number in rectangular form by entering the real component, pressing either plus or minus, the magnitude of the imaginary component and then "2nd" followed by "." to insert the "i" symbol. For example, to enter the number 2 + 3i, press the buttons "2," "+," "3," "2nd" and "." To enter the purely imaginary number "-6i," press the buttons "-," "6," "2nd" and "."

• Enter your number in polar form by entering the complex number's radius (the square root of the real component squared plus the imaginary component squared) and "e" raised to the number's angle (the arctan of the ratio of the imaginary component and the real component) times "i." For example, to enter the number 4e^(2i), press the buttons "4," "2nd," "ln," "2," "2nd" and "."

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