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

P² + 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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Index

8.1 Geometry of complex numbers
8.2 De - Moivres's theorem
8.3 Roots of complex numbers
8.4 Cirsular functions of complex angles & hyperbolic function
Supplementary Problems

Chapter 9