JEE Main 202331 Jan, Evening shiftMathematicsEasyComplex Numbers and Quadratic Equations264× since 2002The complex number z=i−1cosπ3+isinπ3z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}z=cos3π+isin3πi−1 is equal to :AOption A. cosπ12−isinπ12\cos \frac{\pi}{12}-i \sin \frac{\pi}{12}cos12π−isin12πBOption B. 2(cosπ12+isinπ12)\sqrt{2}\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)2(cos12π+isin12π)COption C. 2i(cos5π12−isin5π12)\sqrt{2} i\left(\cos \frac{5 \pi}{12}-i \sin \frac{5 \pi}{12}\right)2i(cos125π−isin125π)DOption D. 2(cos5π12+isin5π12)\sqrt{2}\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)2(cos125π+isin125π)CheckSkip · show solution
