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Precalculus

Complex numbers

Multiply complex numbers like (3 + 4i)(1 − 2i) and find a size (modulus) such as |3 + 4i|.

Open in Trident

A complex number is a + bi, where i is the square root of −1. You can add, subtract, multiply and divide them like ordinary expressions.

Example: (3 + 4i)(1 − 2i) = 3 − 6i + 4i − 8i² = 11 − 2i. The size of 3 + 4i is √(9 + 16) = 5.

Classic Graphing 84

Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.

  1. Type (3 + 4i)(1 − 2i). The i is 2nd then the decimal point key.

    (3+42ndi.)(1−22ndi.)enter

  2. For the size of 3 + 4i: open MATH, move right to NUM, pick 1 abs(, type 3 + 4i and close the bracket.

    math▶13+42ndi.)enter

You should see11-2i abs(3+4i) 5

Classic Graphing 84 key reference · Classic Graphing 84 manual

Natural Scientific 991

Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.

  1. Open the Complex app (MENU, then 2). The i is the ENG key.

    MENU2

  2. Type (3 + 4i)(1 − 2i) and press =.

    (3+4ENG)(1−2ENG)=

You should see11-2i

Natural Scientific 991 key reference · Natural Scientific 991 manual

Natural Color Graphing

Start on the main screen: Press MENU then 1 to open Run-Matrix, the main calculation screen. Press EXIT to back out of a bar or screen, and SHIFT then EXIT (QUIT) to return to the app start.

  1. Open SET UP (SHIFT then MENU), move down three lines to Complex Mode, press F2 for a+bi, then EXIT.

    SHIFTSET UPMENU▼▼▼F2EXIT

  2. Type (3 + 4i)(1 − 2i). The i is ALPHA then the ×10ˣ key. Press EXE.

    (3+4ALPHAi×10ˣ)(1−2ALPHAi×10ˣ)EXE

You should see11-2i

Natural Color Graphing key reference · Natural Color Graphing manual

Classic CAS

Start on the main screen: Press home to open the Home menu (Calculator, Graphs, Settings, and more). Choose Calculator, or press esc to go back to the calculation page.

  1. Type (3 + 4i)(1 − 2i). The i is ctrl then the π key. Press enter.

    (3+4ctrl𝑖π)(1−2ctrl𝑖π)enter

  2. For the size of 3 + 4i, open the catalog and choose abs( (the first entry). Type 3 + 4i, close the bracket and press enter.

    catalogenter3+4ctrl𝑖π)enter

You should see11-2·i abs(3+4i) 5

Classic CAS key reference · Classic CAS manual

RPN Advanced 42

Start on the main screen: Press EXIT (once or twice) to close any menu and return to the plain stack view of Y and X.

  1. Make 3 + 4i: key in 3 ENTER 4, then shift and STO (COMPLEX) join them.

    3ENTER4⇧COMPLEXSTO

  2. Make 1 − 2i the same way: 1 ENTER 2, +/−, shift STO.

    1ENTER2+/−⇧COMPLEXSTO

  3. Press ×.

    ×

You should seex: 11.0000 -i2.0000

RPN Advanced 42 key reference · RPN Advanced 42 manual

RPN Power 48

Start on the main screen: Press ON to cancel what you are typing, then use the stack view. Open the MODE or VAR menu any time; the stack is always shown above the menu row.

  1. Make (3,4): key in 3 ENTER 4, then left shift 1 (R→C).

    3ENTER4◀R→C1

  2. Make (1,-2): key in 1 ENTER 2, +/−, then left shift 1.

    1ENTER2+/−◀R→C1

  3. Press ×.

    ×

You should see(11,-2)

RPN Power 48 key reference · RPN Power 48 manual

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