TI -  89

To convert from Rectangular to Polar Coordinates key [x,y] 2nd MATH 4: Matrix L: Vector ops 4: ► Polar

For example [1, Ö(3)]: ► Polar gives [2 Ð p/3]

To convert from Polar to Rectangular Coordinates key [r,Ðq] 2nd MATH 4: Matrix L: Vector ops 5: ► Rect

For example [2, Ð p/3] ► Rect gives [1 Ö3]

The “Ð ” is 2nd EE. The “,” does not display in the answer, but it is there. See p. 456, 464.

To convert a complex number in standard (i.e. rectangular, i.e. a + bi) form to polar (i.e.. r eiq) form, set the mode to complex polar with MODE Complex Format 3: POLAR, key in the complex number in standard form & press ENTER. The way the result is displayed depends on what modes you are in. You may need to reset the Exact/Approx mode or the Angle mode (i.e. Degree vs. Radian mode). For example:

In exact, radian mode Ö2 + Ö2i ENTER gives 2 eip/4.

In approx, radian mode Ö2 + Ö2i ENTER gives 2 e0.785 i.

In exact, radian mode Ö5 + i ENTER gives       ei arctanÖ5/5 Ö3 Ö2.

In approx, polar, degree mode Ö2 + Ö2i ENTER gives 2.449Ð24.095.

Etc.

Apparently the TI-89 cannot be commanded to display in trigonometric form (e.g. 2 cos 45° + 2i sin 45°).

To convert a complex number in polar (i.e. reiq) form to a complex number in standard (i.e. rectangular, i.e. a + bi) form, set the mode to complex rectangular with MODE Complex Format 2: RECTANGULAR, key in the complex number in standard form and press ENTER. Again the way the result is displayed depends on what modes you are in. For example

In approx mode 2eip/4 ENTER gives 1.414 + 1.414 i.

In exact mode 2eip/4 ENTER gives Ö2 + Ö2i.