[solved] – Question 93483

A number of the form a + ib, in which i2 = -1 and a and b are real numbers, is called a complex
number. We call the real part and b the imaginary part of a + ib. Complex numbers can also be
represented as ordered pairs (a, b). The addition and multiplication of complex numbers are defined
by the following rules:
(a + ib) + (c + id) = (a + c) + i(b + d )
(a + ib) * (c + id) = (ac – bd) + i(ad + bc)
Using the ordered pair notation, these rules are written as:
(a, b) + (c, d) = ((a + c), (b + d ))
(a, b) * (c, d) = ((ac – bd ), (ad + bc))
C++ has no built-in data type that allows us to manipulate complex numbers. Construct a data type,
complex Type, that can be used to process complex numbers. Overload the stream insertion and
stream extraction operators for easy input and output. We will also overload the operators + and *
to perform addition and multiplication of complex numbers. If x and y are complex numbers, we can
evaluate expressions such as x + y and x * y.

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