Evaluate: [(i¹⁸ + (1 / i )²⁵]³

Solution:

We will use the fact of powers of iota here.

[(i18 + (1 / i )25]3 = [ (i2)9  + (-i)25 ]3   [∵ 1/i = 1/i · i/i = i/i2 = i/-1 = -i]

= [(-1)9 - i25] 3   [∵ i2 = -1]

= [-1 - (i2)12 · i]3

= [-1 - (-1)12 · i]3

= (-1 - i)3

= (-1)3 + (-i)3 + 3(-1)(-i) (-1-i)

= -1 + i -3i + 3

= 2 - 2i

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 1

Evaluate: [(i¹⁸ + (1 / i )²⁵]³

Summary:

[(i18 + (1 / i )25]3 = 2 - 2i

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