Question

value of i²⁰ + i¹⁰ ?

help me guys plz​

Answer 1

Answer:

First, understanding what 'i' is, is important.

The notation 'i' refers to √-1.  It is called an imaginary number, since -1 doesn't have roots, nay, no negative number has roots.

Then what about √-2? Well, √-2 is the same as 2 × √-1, and we know √-1 = i, so √-2 is 2i, and so does every other negative number.

So i²⁰ = (√-1)²⁰ = $(-1^{\frac{1}{2} } )^{20}$ = -1¹⁰.

If we multiply -1 twice, it is 1, if thrice, it becomes -1, that means, with even numbers, -1 results in the value 1.

So, i²⁰ = 1

Now i¹⁰, the same way:

= (√-1)¹⁰ = $(-1^{\frac{1}{2} })^{10}$ = -1⁵ = -1.

So,

i¹⁰ = -1.

So, 1²⁰ + i¹⁰ = -1 + 1 = 0

Hope it Helps,

Byeeee