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## Question

Four basic numbers from science and mathematics have the symbols pi, e, 1 and i.

Their values are

pi = 3.1415926536 ...

e = 2.718281828459 ...

1 = unity

i = sqrt[-1]

Arrange these numbers, using them once and only once, so that they equal 0

using only the operations +, ×, and exponentiation.

Use the spoiler, Luke.

## Recommended Posts

• 0 e^(i(pi)) + 1 = 0

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• 0 Four basic numbers from science and mathematics have the symbols pi, e, 1 and i.

Their values are

pi = 3.1415926536 ...

e = 2.718281828459 ...

1 = unity

i = sqrt[-1]

Arrange these numbers, using them once and only once, so that they equal 0

using only the operations +, ×, and exponentiation.

Use the spoiler, Luke.

Are we allowed to use functions ... like ceiling, floor, Int()??

pi*(1+i^floor(e))=0

^ used for exponentiation

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Are we allowed to use functions ... like ceiling, floor, Int()??

Sorry ... just the ones listed. ##### Share on other sites
• 0 1+e^(i*PI)=1+cos(PI)+i(sin(PI)) ... in trigonometric form

which is equal to zero.

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use Euler's identity, which is the special case of Euler's formula, the equation for going around a circle with a real x axis and a nonreal y axis

the special case is:

epi*i + 1 = 0

which comes from this:

epi*i = -1

which comes from this:

etheta*i = cos(theta) + i*sin(theta)

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