Question

what is the value of x when x=i^1+i^2+i^3+....+i^100?​

Answer 1

Answer:

your answer attached in the photo

Answer 2

Hint:

We must know, $i=\sqrt{-1}$ or $i^{2}=-1$

To find:

The value of $x=i^{1}+i^{2}+i^{3}+i^{4}+...+i^{100}$

Step-by-step explanation:

Let us find some value beforehand.

• $i^{1}=i$

• $i^{2}=-1$

• $i^{3}=(i^{2})\times i=(-1)\times i=-i$

• $i^{4}=(i^{2})^{2}=(-1)^{2}=1$

• $i^{5}=(i^{4})\times i=1\times i=i$

• $i^{6}=(i^{2})^{3}=(-1)^{3}=-1$

• $...\:...\:...$

• $i^{100}=(i^{2})^{50}=(-1)^{50}=1$

We see that the sum $(i-1-i+1)$ that is, 0 repeats in the series.

Thus, $x=i^{1}+i^{2}+i^{3}+i^{4}+...+i^{100}$

$=(i-1-i+1)+(i-1-i+1)+...+(i-1-i+1)$

$=0+0+...+0$

= 0

Final answer: $x=0$

$x=0$ when $x=i^{1}+i^{2}+i^{3}+...+i^{100}$

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