Question

If ${log}_e$(A+iB) = $(ilog\sqrt{3}+\frac{\pi }{4})$ .Find the value of A and B.

• A. A = cos() B = sin
• B. A = cos() B = sin
• C. A = B =
• D. A = B =

Answer 1

The correct option is D

A = B =

${log}_e$(A+iB) = i ${log}_e\sqrt{3}+\frac{\pi }{4}$

Taking anti log on both sides

(A+iB) = $e^{\frac{\pi }{4}}.e^{i{log}_e\sqrt{3}}$

= $e^{\frac{\pi }{4}}\left[cos\right({log}_e\sqrt{3})+isin({log}_e\sqrt{3}\left)\right]$

A+iB = $e^{\frac{\pi }{4}}cos\left({log}_e\sqrt{3}\right)+i{e}^{\frac{\pi }{4}}sin\left({log}_e\sqrt{3}\right)$

A = $e^{\frac{\pi }{4}}cos\left({log}_e\sqrt{3}\right)$

B = $e^{\frac{\pi }{4}}sin\left({log}_e\sqrt{3}\right)$