find the inage of (-4, -2) obtained by translating 3 units up, followed by a reflection over the x-axis
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Answer:
<h3>i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰ = 0</h3>Step-by-step explanation:
Consider the sum S = i¹ + i² + i³ +. . .+ i⁹⁹ + i¹⁰⁰
S = i¹ + i² + i³ + . . . + i⁹⁹ + i¹⁰⁰
S = a₁ + a₂ + a₃ +. . . + a₉₉ + a₁₀₀
then, S is the sum of 100 consecutive terms of a geometric sequence (an)
where the first term a1 = i¹ = i and the common ratio = i
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then
or i¹⁰⁰ = (i⁴)²⁵ = 1²⁵ = 1 (we know that i⁴ = 1)
Hence
S = 0
Both claims are false. In fact, and
are one the multiplicative inverse of the other. This means, by definition of multiplicative inverse, that
So, it doesn't matter if is positive or negative: the multiplication of one number and its inverse will always be 1: for example,
Similarly, when you multiply two number, the sign of the product depends on the sign of the factors as follows:
So, the multiplication of two negative numbers is a positive number.