6. Rectangular Form on the Calculator
 

The complex number a + bi has rectangular form (a,b) on the calculator. For example, to enter 3 + 5i into the calculator make sure it is in rectangular coordinate mode then 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 earlier. Key MTH NXT m-CMPL 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) m-RE returns the real part of that complex number and m-IM returns the imaginary part of the complex number on level 1. The function m-C->R takes the complex number from level 1 and puts the real part on level 2 and the imaginary part on level 1 while m-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 2.6.1

We will use the calculator to do Examples 1 and 2 above. For Example 1 , we were to find the rectangular form of  With the calculator set to rectangular coordinates and standard display mode, use the equation writer to key in the polar form of P: LS EQUATION 5 2 RA LS e^x 3 LS  4 RA AS LS I RA 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 rectangular coordinates, standard display mode, degree angle mode, and bring up the complex number menu. Now key 7 +/- ENTER ENTER 3 m-R->C. We should now see (-7,-12.124355653) on the display. Now RS POLAR converts it to polar form and we see  and after LS RAD we convert it to radians and 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 m-ARG LS SYMBOLIC 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 2.6.2

Find |(3 + 7i)(2 - 5i)|. We will first get back into the complex number menu with MTH NXT m-CMPL. We now key in the problem: LS ( ) 3 SPC 7 ENTER LS ( ) 2 SPC 5 +/-  m-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.