In this part we examine how Maple deals with complex numbers.
The imaginary unit is denoted by I (upper-case "eye") in Maple. So, to assign 5+3i to a, enter a := 5 + 3*I;
Enter the following complex numbers in your worksheet:
a = 5 + 3i
b = 2 - 4i
c = - 3 + i
d = - 2 - 4i
Enter the following lines of Maple code, and describe what each of the Maple commands does. Check by trying with a number different from a.
Re(a);
Im(a);
abs(a);
conjugate(a);
The argument function needs special attention. Enter each of the following:
argument(a);
argument(b);
argument(c);
argument(d);
What is the range of the argument function? Describe carefully what the argument function does.
It is often useful to consider complex numbers in their polar form. Enter the following: ap := convert(a,polar);
What are the components of the result? Repeat this for bp := convert(b,polar);
The command evalc ("evaluate in complex form" ) converts in the other direction. Enter evalc(ap);
Calculate the polar form of ab. How is the polar form of the product related to the polar forms of the factors?
