Imaginary and complex numbers on your calculator. Source. Use the MODE key to place the calculator in a+b i mode. The complex i is found above the decimal point key or in the catalog. Note: .
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Note: • Complex numbers can be accessed from Real Mode(without placing calculator in a+ bi Mode). Real mode, however, does not display complex results unless complex numbers are entered as input. For example, if the calculator is NOT in a + bi Mode, will create an error. You get an error message when you try to enter the square root of a negative number when in Real Mode.
Note: • You need to be in a + bi mode to evaluate the square root of a negative number.
Arithmetic of Complex Numbers • Add: (2 + 4i) + (3 - 2i) • Subtract: (6 - 3i) - (4 + 5i)
Arithmetic of Complex Numbers • Multiply:(3 + 2i) (4 - 2i)
Note: • For TI-83+ and for TI-84+ with OS prior to OS 2.53MP. • In this display, iis NOT in the denominator! The calculator is simply listing order of operations.
Note: • TI-84+ with OS 2.53MP
Note: • Be careful to write your final answer correctly. Note the location of thei in the final answer: • Note: On OS2.53MP, if the decimals you are trying to "grab" to convert to fractions are really long, use MATH - CPX - real( and imag( to "grab" the full decimal value for converting "a" and "b" to fractions.
Powers of i • These values will appear when you are in either Real Mode or in a + bi mode.
Powers of i • You can look at many powers at once by using a list • …use right arrow to scroll to the right to see all of the answers
Note: • What kind of number is - 3E - 13 - i??? • This number is really just - i.- 3E - 13 is so small, it is considered to be zero. • (E-13 is Scientific Notation meaning 10 raised to -13 power.)
Beware! • When raising i to a power on a graphing calculator, accuracy diminishes as the powers increase.
Special Calculator Functions for Complex Numbers • 1. conj( returns the complex conjugate of a complex number.conj(2+5i) gives 2-5i • 2. real( returns the "a" value in an a+bicomplex number.real(2+5i) gives 2 • 3. imag(returns the "b" value in an a+bicomplex number.imag(2+5i) gives 5 • 5. abs(returns the absolute value of the complex number.abs(5+12i) gives 13
Note: • The absolute value of a complex number may also be called its magnitude. It you plot a complex number as a single point, the absolute value represents the distance from the origin to that point. If you plot a complex number as a vector, the absolute value represents the length of the vector