i+i²+i³+i⁴=?

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i+i²+i³+i⁴=?

Guest May 10, 2015

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Best Answer

i+i²+i³+i⁴ = ?

$\begin{array}{rcl} i+i^2+i^3+i^4&\\ &=& {( \underbrace{ 1+\underbrace{i^2}_{=-1} }_{=0} ) \cdot(i+i^2)\\ i+i^2+i^3+i^4&=& 0 \end{array}$

heureka May 10, 2015

heureka · Answer 1 · 2015-05-10T02:43:53

i+i²+i³+i⁴ = ?

$\begin{array}{rcl} i+i^2+i^3+i^4&\\ &=& {( \underbrace{ 1+\underbrace{i^2}_{=-1} }_{=0} ) \cdot(i+i^2)\\ i+i^2+i^3+i^4&=& 0 \end{array}$

CPhill · Answer 2 · 2015-05-10T03:43:18

0...believe it, or not !!!

To see why.......

i^1 = i

i^2 = -1

i^3 = i^2 * i = -1i = -i

i^4 = i^2 * i^2 = -1 * -1 = 1

Notice...that when we add "like" terms....they all "cancel" to 0 !!!!