HP 39GS HP 39gs_40gs_Mastering The Graphing Calculator_English_E_F2224-90010.p - Page 299
Method 3 - Using the POLYROOT function, Finding complex solutions to a complex equation
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Method 3 - Using the POLYROOT function The advantage of this is that it can be done in the HOME view and is quick and easy. It also has the advantage that it returns complex roots as well. See page 84 for a method of copying the results to a matrix so as to gain easier access to them. This method is highly recommended for polynomials in general. Finding complex solutions to a complex equation Find the roots of the complex equation f (z) = z2 + z +1. Method 1 - Using the QUAD function Since this is a quadratic it can be done with the QUAD formula mentioned in example 1., since it is capable of giving complex results. This is shown right, rounded to 4 dec. pts. It's up to you of course to realize that (0,1.7321) is 3 i but if you don't recognize it then just that portion and square it. The 'S1' means ± . The only real advantage of this method is that it gives the answer in the same format as the quadratic formula and this may be of use. Method 2 - Using POLYROOT An alternative method is to use the POLYROOT function and store the results to a matrix. This offers the advantage of being able to examine the result more easily by ing the matrix, and also of being able to access each root by referring to the matrix elements in a calculation (eg M1(1), M1(2) etc.). See page 84 for more details on this. The disadvantage of this method is that for higher degree polynomials with a mixture of real and complex roots, all roots are shown in complex form. This can make the real roots harder to isolate and use. However, it is still the best method. Method 3 - Using the CAS on the hp 40gs See page 309 for an example of finding roots of real and complex polynomials using the CAS on the hp 40gs. 299