Question:medium

Principal Values of Logarithmic Functions

CaseComplex NumberPrincipal Value
A\(\log(-2)\)\(\log 2 + i\pi\)
B\(\log(5i)\)\(\log 5 + \dfrac{i\pi}{2}\)
C\(\log(\sqrt{3}-i)\)\(\log 2 - \dfrac{i\pi}{6}\)
D\(\log(2-3i)\)\(\dfrac{1}{2}\log 13 - i\tan^{-1}\left(\dfrac{3}{2}\right)\)

 

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For complex logarithm, first find modulus and principal argument: \(\log z=\log r+i\theta\).
Updated On: May 20, 2026
  • A, B
  • B, C
  • B, D
  • A, D
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The Correct Option is C

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