Evaluate the [i 41 + 1/i 257]

Question

Evaluate the \( i^{41 }+ \dfrac{1}{i^{257}}\)

Asked by Aaryan | 1 year ago | 116

0 0

Class 11 Maths Complex Numbers and Quadratic Equations Add Answer

Show that 1 + i¹⁰ + i²⁰ + i³⁰ is a real number?

Solve the quadratic equations by factorization method only 6x² – 17ix – 12 = 0

Solve the quadratic equations by factorization method only x² + (1 – 2i)x – 2i = 0

Solve the quadratic equations by factorization method only x² + 10ix – 21 = 0

Solve the quadratic equations by factorization method only 17x² – 8x + 1 = 0

Accepted Answer

Let us simplify we get,

= \( \dfrac{i^{40}+1 + 1}{ i^{256}+1}\)

=\( [i + \dfrac{1}{i}]^9\) [since, \( \dfrac{1}{i}\) = -1]

= [i – i]

= 0

Answered by Aaryan | 1 year ago