For any integer \(n\) the argument of \[z=\dfrac{(\sqrt{3}+i)^{4n+1}}{(1-i\sqrt{3})^{4n}}\] is:- \[(a)\dfrac{\pi}{6}\]

\[(b)\dfrac{\pi}{3}\]

\[(c)\dfrac{\pi}{2}\]

\[(d)\dfrac{2\pi}{3}\]

This question is based on COMPLEX NUMBERS..

Please post the solution in Detail...

No vote yet

1 vote

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest\(z=\dfrac{(2 cis (\frac{\pi}{6}))^{4n+1}}{(2 cis (-\frac{\pi}{3}))^{4n}}\)

\(z=\left(\dfrac{2 cis (\frac{\pi}{6})}{2 cis (-\frac{\pi}{3})}\right)^{4n} 2 cis (\frac{\pi}{6})\)

\(z=2(cis (\frac{\pi}{2}))^{4n} cis (\frac{\pi}{6})\)

\(z=2(i)^{4n} cis (\frac{\pi}{6})\)

\(z=2 cis (\frac{\pi}{6})\)

\(\arg z = \boxed{\dfrac{\pi}{6}}\)

Log in to reply

Is the Answer Pi/6 ???

Log in to reply