i is an imaginary number and ln is a natural logarithm. How come -i·ln(-1) = π?
e^(iπ) = -1
ln(-1) = iπ
ln(-1) / i = π
ln(-1)(i ⁻¹) = π
Note that i ⁻¹ = -i
since i = √(-1) and 1 / i = 1 / (√(-1)) = 1 / (√(-1))∙((√-1) / (√-1)) since ((√-1) / (√-1)) = 1
1 / (√(-1))∙((√-1) / (√-1)) = 1√(-1) / i² = i / (-1) = -i
∴ (i ⁻¹)ln(-1) = (-i)ln(-1) = π
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Verified answer
e^(iπ) = -1
ln(-1) = iπ
ln(-1) / i = π
ln(-1)(i ⁻¹) = π
Note that i ⁻¹ = -i
since i = √(-1) and 1 / i = 1 / (√(-1)) = 1 / (√(-1))∙((√-1) / (√-1)) since ((√-1) / (√-1)) = 1
1 / (√(-1))∙((√-1) / (√-1)) = 1√(-1) / i² = i / (-1) = -i
∴ (i ⁻¹)ln(-1) = (-i)ln(-1) = π