ln(z-i)lnz+2=0

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Solution for ln(z-i)lnz+2=0 equation:


Simplifying
ln(z + -1i) * lnz + 2 = 0

Reorder the terms:
ln(-1i + z) * lnz + 2 = 0

Reorder the terms for easier multiplication:
ln * lnz(-1i + z) + 2 = 0

Multiply ln * lnz
l2n2z(-1i + z) + 2 = 0
(-1i * l2n2z + z * l2n2z) + 2 = 0
(-1il2n2z + l2n2z2) + 2 = 0

Reorder the terms:
2 + -1il2n2z + l2n2z2 = 0

Solving
2 + -1il2n2z + l2n2z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -1il2n2z + -2 + l2n2z2 = 0 + -2

Reorder the terms:
2 + -2 + -1il2n2z + l2n2z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1il2n2z + l2n2z2 = 0 + -2
-1il2n2z + l2n2z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1il2n2z + l2n2z2 = -2

Add '-1l2n2z2' to each side of the equation.
-1il2n2z + l2n2z2 + -1l2n2z2 = -2 + -1l2n2z2

Combine like terms: l2n2z2 + -1l2n2z2 = 0
-1il2n2z + 0 = -2 + -1l2n2z2
-1il2n2z = -2 + -1l2n2z2

Divide each side by '-1l2n2z'.
i = 2l-2n-2z-1 + z

Simplifying
i = 2l-2n-2z-1 + z

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