Argument of z if z-sin-5-i1-cos-5 is

Given: z=sin(π5)+i(1 cos(π5)) =2sin(π10)cos(π10)+ i· 2sin ^2(π10) =2sin(π10) [cos(π10)+ isin(π10)] which is of form z=|z|(cosθ + isinθ ) ∴(z) =π10 , |z|=2sin(π ...

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Standard XII

Mathematics

Geometrical Representation of a Complex Number

Argument of z...

Question

Argument of $z$ if $z = sin (\frac{π}{5}) + i (1 - cos (\frac{π}{5}))$ is

\frac{π}{5}

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\frac{π}{10}

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\frac{π}{15}

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\frac{π}{20}

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Solution

The correct option is B $\frac{π}{10}$
We have $z = sin (\frac{π}{5}) + i (1 - cos (\frac{π}{5}))$
$= 2 sin (\frac{π}{10}) cos (\frac{π}{10}) + i \cdot 2 {sin}^{2} (\frac{π}{10})$
$= 2 sin (\frac{π}{10}) [cos (\frac{π}{10}) + i sin (\frac{π}{10})]$

which is of form $z = | z | (cos θ + i sin θ)$
$∴ arg (z) = \frac{π}{10}, | z | = 2 sin (\frac{π}{10})$

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Geometrical Representation of a Complex Number

Standard XII Mathematics

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Argument of z if z=sin(π5)+i(1−cos(π5)) is

The correct option is B π10We have z=sin(π5)+i(1−cos(π5)) =2sin(π10)cos(π10)+i⋅2sin2(π10) =2sin(π10)[cos(π10)+isin(π10)] which is of form z=|z|(cosθ+isinθ) ∴arg(z)=π10,|z|=2sin(π10)

Argument of $z$ if $z = sin (\frac{π}{5}) + i (1 - cos (\frac{π}{5}))$ is