EXAMPLE 4 Prove that (l + j)^{8}+ (l  j)^{8}
= 32
Solution
Now l + j Þ x = 1 and y = 1 ..
(1st  Quad)
EXAMPLE 5 Prove that (1 + cos q
+ j sin q)^{n} + ( 1 + cos q
 j sin q)^{n}
=
2^{n + 1} cosn (q / 2) cos (n
q / 2)
Solution
EXAMPLE 6 If P be a real and the complex number
be represented by a point in the Argand's diagram on the line x
= y.
Show that P =
Solution
But the point is on the line y = x Þ
x = y
P^{2} + 10P + 4 = 0 Solving we get P =
EXAMPLE 7
Perform graphically the following operations
(a) ( 1 + 3i) + (5 + 4i) (b) (2 + 3i) + (l  2i) (c) (3 + 2i)
 (l + i)
(d) (3 + 2i)  (2  i)
Solution
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