Find the values of the expressions i49 + i68 + i89 + i110

Question

Find the values of the expressions i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰

Asked by Sakshi | 1 year ago | 80

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Class 11 Maths Complex Numbers and Quadratic Equations Add Answer

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Accepted Answer

i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰

Let us simplify we get,

i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰= i ^{(48 + 1)} + i⁶⁸ + i^{(88 + 1)} + i^{(108 + 2)}

= (i⁴)¹² × i + (i⁴)¹⁷ + (i⁴)²² × i + (i⁴)²⁷ × i²

= i + 1 + i – 1 [since i⁴ = 1, i² = – 1]

= 2i

i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰ = 2i

Answered by Aaryan | 1 year ago