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Complex Numbers question

2023 · 31 Jan · Shift 2 · Q30

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PYQ Library
JEE Main
Mathematics
Complex Numbers
2023 · 31 Jan · Shift 2 · Q30

Complex Numbers question

2023 · 31 Jan · Shift 2 · Q30

JEE MainMathematicsComplex NumbersMCQ+4 / −1

The complex number

z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}

is equal to :

A
$\cos \frac{\pi}{12}-i \sin \frac{\pi}{12}$
B
$\sqrt{2}\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)$
C
$\sqrt{2} i\left(\cos \frac{5 \pi}{12}-i \sin \frac{5 \pi}{12}\right)$
D
$\sqrt{2}\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)$

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