The natural log of the complex number z = 5 + 7i is 2.152 + 0.951i. To arrive at this answer, follow these steps:
Find the magnitude of z = 5 + 7i, to get |z| = √(52+ 72) = 8.602.
Compute the phase angle of z = 5 + 7i, to get ϕ = tan-1(7/5) = 0.951 rad.
Use the complex natural log formula ln(z) = ln|z| + iϕ to get ln(5+7i) = ln|8.602| + i0.951 = 2.152 + 0.951i.
You can verify your result with our imaginary number calculator.
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