Using Euler's formula

Algebra Level pending

\( \ln(\frac{\sqrt{3}}{2}+\frac{1}{2}i) \times \ln(\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}i) \times \ln(\frac{1}{2}+\frac{\sqrt{3}}{2}i) \times \ln(i) = \large \frac{\pi^{4}}{k^{2}}\)

Find the value of \(|k|\).

(The radian range: \(0 \leq x \leq \pi \))

Hints: \(e^{i(\pi)} = \cos(\pi)+i\sin(\pi) = -1\) \(\Rightarrow\) \(\ln(-1)=i\pi\)

Reference : Euler's Formula

×

Problem Loading...

Note Loading...

Set Loading...