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Linear Functions

29. Find Arg(...

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29. Find Arg( sin8Π/5 + i [ 1+ cos 8Π/5] )

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Q. The principal value of arg z where

z = 1 + cos \frac{6 π}{5} + i sin \frac{6 π}{5}

z = \cos \frac{π}{4} + i \sin \frac{π}{6}

|z| = 1, a r g (z) = \frac{π}{4}

|z| = 1, a r g (z) = \frac{π}{6}

|z| = \frac{\sqrt{3}}{2}, a r g (z) = \frac{5 π}{24}

|z| = \frac{\sqrt{3}}{2}, a r g (z) = \tan^{- 1} \frac{1}{\sqrt{2}}

Find the reciprocal (or multiplicative inverse) of -2 + 5i

z = \frac{1 + i \sqrt{3}}{2 i (cos \frac{π}{3} + i sin \frac{π}{3})},

{cos}^{- 1}

\frac{8 π}{7}

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