If x - cos-6 - isin-6- then

The correct option is B | x | = 1,org z = π/6 x=cosπ6 + i sinπ6 If a complex number is an z=a+ib Then arg z =tanθ #160; =b/a ...

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Standard XII

Mathematics

Modulus of a Complex Number

If x = cosπ...

Question

If $x = cos \frac{π}{6} + i sin \frac{π}{6}$ , then

| x | = 1, o r g z = \frac{π}{4}

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| x | = 1, o r g z = \frac{π}{6}

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| x | = \frac{\sqrt{3}}{2}, o r g z = \frac{5 π}{24}

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| x | = \frac{\sqrt{3}}{2}, o r g z = {tan}^{- 1} \frac{1}{\sqrt{3}}

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Solution

The correct option is B $| x | = 1, o r g z = \frac{π}{6}$
$x = cos \frac{π}{6} + i sin \frac{π}{6}$

If a complex number is an

$⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ \begin{matrix} z = a + i b T h e n a r g z = tan θ = b / a a n d | z | = \sqrt{a^{2} + b c} . \end{matrix} ⎫ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎬ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎭$

So, arg of $x = tan θ = \frac{sin π / 6}{cos π / 6} = tan π / 6$

$tan θ = tan π / 6$

arg of $x = θ = \frac{π}{6}$

and $| x | = \sqrt{c o s \frac{π}{6} + sin \frac{π}{6}} = \sqrt{1} = 1$

So, Option $B$

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