4. Negative of a Point, Subtraction, Conjugate
 

As in other number systems, if P + N = O, one writes N = -P and calls N the negative of P. It follows from the definition of addition of points in the Argand Plane that N is the point such that the directed line segment  has the same magnitude and direction as  i.e., N is the point such that O is the midpoint of segment PN. If  then clearly  See Figure 6.

The difference E - F is the point G such that E = F + G. One can also obtain the difference G = E - F using the formula G = E + (-F). See Figure 7.
 

Figure 7

Figure 8

In the Argand Plane, the conjugate of a point  is the point  with the same absolute value as P but with the argument the negative of that of P. Note that a point P and its conjugate  are symmetrically situated with respect to the straight line determined by O and U. See Figure 8.

These concepts are all easily handled on the calculator. The +/- key converts the complex number in level 1 of the stack to its negative. Enter your favorite complex number and try it! Note that pressing +/- twice returns the original number as it should. The - key will subtract the complex number in level 1 from the complex number in level 2. Try it with your choice of complex numbers A and B. After computing S = A - B, verify that S + B returns your original A. There is also a conjugate function, but it is in one of the menus. Key in MTH NXT m-CMPL NXT and you will find CONJ as the last item in the menu. Key in a complex number and try it. Again, pressing it twice gives back the original complex number as expected.

There are two other functions on this menu page; NEG and SIGN. NEG works the same as the +/- key and SIGN converts the complex number on level 1 into a complex number with the same argument but with absolute value 1. Press NXT and you see six more functions related to complex numbers. The first four will be discussed after the next section, but ABS returns the absolute value of the complex number on level 1, and ARG returns its argument.