Question

I^3+i^13+i^23+i^33+i^43+i^53 вычислить​

Answer 1

Ответ:

0

Пошаговое объяснение:

Решение в приложении.

Answer 2

To simplify the expression and calculate the value, let's consider the pattern of powers of "i":

i^1 = i i^2 = -1 i^3 = -i i^4 = 1

As you can see, the powers of "i" repeat after every 4th power. So, we can rewrite the expression by simplifying the exponents:

i^3 = -i i^13 = i^(12 + 1) = i^12 * i^1 = (i^4)^3 * i = 1^3 * i = i i^23 = i^(20 + 3) = i^20 * i^3 = (i^4)^5 * i^3 = 1^5 * (-i) = -i i^33 = i^(32 + 1) = i^32 * i^1 = (i^4)^8 * i = 1^8 * i = i i^43 = i^(40 + 3) = i^40 * i^3 = (i^4)^10 * i^3 = 1^10 * (-i) = -i i^53 = i^(52 + 1) = i^52 * i^1 = (i^4)^13 * i = 1^13 * i = i

Now, let's sum up all the simplified terms:

i^3 + i^13 + i^23 + i^33 + i^43 + i^53 = (-i) + i + (-i) + i + (-i) + i

When we group the terms with like signs:

(-i + i) + (-i + i) + (-i + i) = 0 + 0 + 0 = 0

So, the final value of the expression is 0.