The principal argument of the complex number z- 1-sin- 3 -icos- 3 1-sin- 3 -icos- 3

The correct option is B π6 arg(z) = arg(Numerator) arg(Denominator) #160; #160;= #160; tan^ 1|cos π31+sin π3| + tan^ 1|cos π31+sin π3| ...

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Modulus of a Complex Number

the principal...

Question

the principal argument of the complex number $z = \frac{1 + sin \frac{π}{3} + i cos \frac{π}{3}}{1 + sin \frac{π}{3} - i cos \frac{π}{3}}$

\frac{π}{3}

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\frac{π}{6}

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\frac{2 π}{3}

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\frac{π}{2}

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{⎛ ⎜ ⎜ ⎝ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{\frac{8}{3}}

- 1

{⎡ ⎢ ⎢ ⎣ \frac{1 + sin \frac{π}{8} + i cos \frac{π}{8}}{1 + sin \frac{π}{8} - i cos \frac{π}{8}} ⎤ ⎥ ⎥ ⎦}^{8} =

\frac{cos 0 \cdot sin \frac{π}{2} \cdot {cos}^{2} (\frac{π}{6}) \cdot {sec}^{2} (\frac{π}{4})}{tan \frac{π}{3} + cot \frac{π}{3}}

The principle argument of the complex number $- 1 - \sqrt{3} i$ is

The argument of the complex number -1-i√3

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