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SSC Pure Mathematics QUESTION #11151
Question 1
$\log(1+i) =$
  • $\dfrac{1}{2}\ln 2 + \dfrac{\pi i}{4}$✔️
  • $\dfrac{1}{2}\ln 2 - \dfrac{\pi i}{4}$
  • $\dfrac{1}{2}\ln 2 - \dfrac{3\pi i}{4}$
  • $\dfrac{1}{2}\ln 2 + \dfrac{3\pi i}{4}$
Correct Answer Explanation
$|1+i| = \sqrt{2}$, $\arg(1+i) = \dfrac{\pi}{4}$ (principal value). Therefore $\text{Log}(1+i) = \ln\sqrt{2} + i\dfrac{\pi}{4} = \dfrac{1}{2}\ln 2 + \dfrac{\pi i}{4}$.