Programming Using C Homework 2
1. Write a simple calculator program for complex numbers. Each complex
number can be seen as a point in
R
2
, written as
a
+
bi
, where
a, b
∈
R
are the real and imaginary parts and
i
=
√

1 is the unitary imaginary
number.
To add and subtract two complex numbers, add or subtract
respectively their real and imaginary parts, i.e., (
a
+
bi
) + (
c
+
di
) =
(
a
+
c
) + (
b
+
d
)
i
.
To multiply, use the distributivity rule, obtaining
(
a
+
bi
)(
c
+
di
) = (
ac

bd
) + (
ad
+
bc
)
i
.
Finally, to divide, amplify
the fraction such that the denominator becomes a real number:
a
+
bi
c
+
di
=
(
a
+
bi
)(
c

di
)
(
c
+
di
)(
c

di
)
=
bd
+
ac
c
2
+
d
2
+
cb

ad
c
2
+
d
2
i
.
The program will work in a loop that
presents a menu of choices, waits for the user’s choice, accepts two complex
numbers, carries out the computation and prints the result.
The menu
choices are: 0 for exiting the program, 1 for addition, 2 for subtraction,
3 for multiplication and 4 for division.
The program should check for
division by 0 + 0
i
, which is undefined.
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 Summer '08
 Staff
 Complex number, cipher text, Golden ratio

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