Question

Find the value of i⁴⁹+i⁶⁸+i⁸⁹+i¹¹⁰

Answer 1

Answer:

i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰ = 2i

Solution:

∴ i⁴⁹ + i⁶⁸ + i⁸⁹ + i¹¹⁰

= i⁴⁸⁺¹ + i⁶⁸ + i⁸⁸⁺¹ + i¹¹⁰

= i⁴⁸.i + i⁶⁸ + i⁸⁸.i + i¹¹⁰

= (i²)²⁴.i + (i²)³⁴ + (i²)⁴⁴.i + (i²)⁵⁵

= (- 1)²⁴.i + (- 1)³⁴ + (- 1)⁴⁴.i + (- 1)⁵⁵

= 1.i + 1 + 1.i - 1

= i + 1 + i - 1

= 2i , which is the required value.

Now if we want to find the modulus value, we find the modulus value of 2i, which is given by

| 2i | = √(0² + 2²) = 2

Note:

Here i = √(- 1) and i² = - 1