bonanova 85 Posted March 7, 2008 Report Share Posted March 7, 2008 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. Quote Link to post Share on other sites

0 Guest Posted March 7, 2008 Report Share Posted March 7, 2008 e^(i(pi)) + 1 = 0 Quote Link to post Share on other sites

0 Guest Posted March 7, 2008 Report Share Posted March 7, 2008 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 Quote Link to post Share on other sites

0 bonanova 85 Posted March 7, 2008 Author Report Share Posted March 7, 2008 Are we allowed to use functions ... like ceiling, floor, Int()?? Sorry ... just the ones listed. Quote Link to post Share on other sites

0 Guest Posted March 7, 2008 Report Share Posted March 7, 2008 1+e^(i*PI)=1+cos(PI)+i(sin(PI)) ... in trigonometric form which is equal to zero. Quote Link to post Share on other sites

0 unreality 1 Posted March 7, 2008 Report Share Posted March 7, 2008 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: e^{pi*i} + 1 = 0 which comes from this: e^{pi*i} = -1 which comes from this: e^{theta*i} = cos(theta) + i*sin(theta) Quote Link to post Share on other sites

## Question

## bonanova 85

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.

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