7. Rectangular Form on the Calculator

If the calculator is still in polar mode from the previous section, press MODE and change the Coordinate system back to Rectangular. The complex number a + bi has rectangular form (a,b) on the calculator. For example, to enter 3 + 5i into the calculator key in LS ( ) 3 SPC (one could key in the comma here instead of SPC, but that would take two key strokes and the calculator will turn the space into a comma anyway) 5 ENTER. At this point we can also discuss the first four functions in the complex number menu which were mentioned in the previous section. Key LS MTH NXT F3-CMPLX to get back into the complex number menu. Assuming there is a complex number on level 1 of the stack (with the calculator in either rectangular or polar mode) F1-RE returns the real part of that complex number and F2-IM returns the imaginary part of the complex number on level 1. The function F3-C->R takes the complex number from level 1 then puts the real part on level 2 and the imaginary part on level 1 while F4-R->C reverses that process. It takes a real number from level 2 as the real part and a real number from level 1 as the imaginary part and forms a complex number which it puts on level 1.

Calculator Example 2.7.1

We will use the calculator to do Examples 1 and 2 from Section 5 of this chapter. For Example 1, we were to find the rectangular form of With the calculator set to rectangular mode and standard display, use the equation writer to key in the polar form of P: RS EQW 5 2 RA LS e^x 3 4 RA LS i ENTER EVAL. The result will be (-4.99999999998,5). The real part should, of course, be -5, but we are seeing the unavoidable roundoff errors which occur when we use a finite device to approximate real numbers.

For Example 2 we were to find the polar form for We will place the real part on level 2 of the stack and the imaginary part on level 1, then use the R->C command to create the complex number. Set the calculator to polar coordinates, standard display, radian angle mode, and bring up the complex number menu. Now key 7 +/- ENTER ENTER 3 F4-R->C. We should now see There is one more thing we can try which sometimes gives us an answer in a form we would like to see it. Key F6-ARG LS CONVERT F4-REWRI NXT and we see on the display. The command works to convert a decimal expression into a rational number times if it's not to far from one of the "nice" angles. If, however, you compute as a decimal then try to get it back, you get a very strange result.

Calculator Example 2.7.2

Find |(3 + 7i)(2 - 5i)|. We key in the problem: LS ( ) 3 SPC 7 ENTER LS ( ) 2 SPC 5 +/- LS ABS. We see the answer 41.0121933088. Notice that it doesn't matter if the calculator is in rectangular or polar coordinates when we key in the problem.