A complex number problem

Geometry Level 3

The argument of the complex number sin ⁡ 6 π 5 + i ( 1 + cos ⁡ 6 π 5 ) = \displaystyle\sin \frac{6\pi}{5} + i\left(1+\cos \frac{6\pi}{5}\right) =
Where i i denotes − 1 \sqrt{-1} .

2 5 π \frac25 \pi 9 10 π \frac9{10} \pi 5 6 π \frac56 \pi 6 5 π \frac65 \pi

Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Kumar Krish
Jan 5, 2019

Find tan (y/x) and then find in which quadrant the complex no. Is lying Here the complex number is lying in 2nd quadrant so principal argument is π-(smallest positive angle satisfying tan(y/x)

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