Example 3
Solve x^{9}  x^{5} + x^{4}  1 = 0
Solution
x^{9}  x^{5}+ x^{4}  1 = x^{5}
(x^{4}  1) + 1(x^{4}  1) = (x^{5}+ 1)
(x^{4} 1)
Now the 1st factor,
x^{5} + 1 = 0 Þ x^{5}
= 1 = cos (2k + 1) p + i sin (2k + 1)p
Example 4
Solve x^{12}  1 = 0 and which of its roots satisfy the
equation x^{4} + x^{2} + 1 = 0
Solution
Therefore these roots satisfy both x^{12}  1 = 0 and
x^{4} + x^{2}+ 1 = 0
Example 5
If a and b
are roots of x^{2}  2x + 4 = 0. Find a^{n}
+ b^{n}. Hence a^{15}
+ b^{15}
Solution
Example 6 Find all values of (1 + i)^{1/3}and represent
them on the Argand's diagram.
Solution
Thus z1 , z2 and z3 are the required all values of (l + i)1/3^{
}
They are represented on the Argand's diagram as
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