Question

Вычислить: i^2+2i^4-i^22+i^36

Answer 1

i^2 + 2i^4 - i^22 + i^36 = 3

Answer 2

To calculate the given expression, we need to remember the properties of the imaginary unit 'i':

1. i^2 = -1
2. i^4 = (i^2)^2 = (-1)^2 = 1
3. i^6 = i^4 * i^2 = 1 * (-1) = -1

Now, let's compute the expression step by step:

i^2 + 2i^4 - i^22 + i^36

1. i^2 = -1
2. 2i^4 = 2 * 1 = 2
3. i^22 = (i^6)^3 * i^4 = (-1)^3 * 1 = -1
4. i^36 = (i^6)^6 = (-1)^6 = 1

Now, substitute these values back into the expression:

-1 + 2 - (-1) + 1

Combine the terms:

-1 + 2 + 1

Finally, add the numbers together:

2

So, the value of the expression is 2.