math problem
November 11th, 2013 at 7:38:19 AM
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Using approximation exp(PI)=25 (that is an 8% correction)
Calculate i^( exp(i*PI) +5*i^i)=?
Calculate i^( exp(i*PI) +5*i^i)=?
November 11th, 2013 at 10:05:02 AM
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First, substitute -1 for ei * PI:
i-1 + 5 * ii
Next, replace ix with ex ln i:
i-1 + 5 * ei ln i
e(-1 + 5 * ei ln i) * ln i
Next, substitute i * PI/2 for ln i:
e(-1 + 5 * ei * i * PI/2) * i * PI/2
e(5 * e-PI/2 - 1) * i * PI/2
ei * (PI/2 * (5 * e-PI/2 - 1)))
If epi = 25, then e-PI/2 = 1/5:
ei * (PI/2 * (5 * 1/5 - 1)))
ei * (PI/2 * 0)
which is e0 = 1
i-1 + 5 * ii
Next, replace ix with ex ln i:
i-1 + 5 * ei ln i
e(-1 + 5 * ei ln i) * ln i
Next, substitute i * PI/2 for ln i:
e(-1 + 5 * ei * i * PI/2) * i * PI/2
e(5 * e-PI/2 - 1) * i * PI/2
ei * (PI/2 * (5 * e-PI/2 - 1)))
If epi = 25, then e-PI/2 = 1/5:
ei * (PI/2 * (5 * 1/5 - 1)))
ei * (PI/2 * 0)
which is e0 = 1
