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Number Theory Level 2

What is the value of this expression ?????

i 0 1 2 π \pi ∞ \infty

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Gagan Raj by Gagan Raj , 23, India

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2 solutions

Gagan Raj
Feb 21, 2015

Commonly known as Euler's Identity or Euler's Equation , this is a special case of Euler's Formula.

Euler's Formula is :-

e i x e^{ix} = c o s x + i s i n x cos{x} + isin{x}

when x x = π \pi

we get the above expression commonly called as Euler's Identity.

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By Euler

we know that e i π = − 1 e^{i \pi} = -1

Hence, − 1 + 1 = 0 -1+1 =0

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