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8.54 Implement the following additional constructor for the Complex class (Problem 8.25): Complex(Rationa1);

Fig. 4-65

Rational Complex x(22,7); z(x);

In Fig. 4-65, find the distance (a) from P to the outer circle; (b) from P to the inner circle; (c) between the concentric circles; (d) from P to O. (4.6) In Fig. 4-66 (4.6)

would construct the Rat ional object x that represents the fraction 22/7 and the Complex object z that represents the real number 3.14159. 8.55 Implement the following additional functions for the Point class (Problem 8.17):

(a) Locate P, a point on AD, equidistant from B and C. Then locate Q, a point on AD, equidistant from AB and BC. (b) Locate R, a point equidistant from A, B, and C. Then locate S, a point equidistant from B, C, and D. (c) Locate T, a point equidistant from BC, CD, and AD. Then locate U, a point equidistant from AB, BC, and CD. 4.10. In each part of Fig. 4-67, describe P, Q, and R as equidistant points and locate them on a bisector.

float Point dot(Point); cross(Point);

The dot ( > function returns the dot product (scalar product), and the cros s ( > returns the cross product (vector product).

Fig. 4-66

EXAMPLE 4.12 TIMED EVENTS (A METRONOME)

8.57 Modify the String class (Problem 8.21) by adding the function String substr(short start, short length);

Fig. 4-67

This function returns the String object that contains the substring of the owner indexed from startto start + length - 1. For example, if s represents the string I ABCDEFGHI JK I , then s . subs tr (2,s ) would return the object that represents the string YDEFG II, and s . subs tr ( 8 ,7 ) would return the object that represents the string I I JK I . Note that the value of start is the length of the omitted prefix.

In each part of Fig. 4-68, describe P, Q, and R as equidistant points. (4.9)

8.59 Implement a Quaternion class for hypercomplex numbers (also called hamiltonians ). Each object of this class will represent a hypercomplex number t + x i + y j + z k, where each of the components t, X, y, and z has type double. Include a default constructor, a copy constructor, access functions, a norm ( > function that returns the norm (magnitude) of the hypercomplex number, an isEqualTo (Quaternion) function, and arithmetic functions plus (Quaternion), minus(Quaternion) ,and times(Quaternion) ,where multiplication is defined

Fig. 4-68

Write a program like the one in Example 8.2, except insert the new nodes at the end of the list so that the data values can be input in the same order as they are output.

Find x and y in each part of Fig. 4-69.