# JEE Main & Advanced Mathematics Complex Numbers and Quadratic Equations Question Bank

### done Square root, Representation and Logarithm of complex numbers

• A) $\frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}}$

B) $\frac{a+b}{c+d}$

C) $\frac{{{c}^{2}}+{{d}^{2}}}{{{a}^{2}}+{{b}^{2}}}$

D) ${{\left( \frac{{{a}^{2}}+{{b}^{2}}}{{{c}^{2}}+{{d}^{2}}} \right)}^{2}}$

• A) $1\pm 3i$

B) $\pm (1-3i)$

C) $\pm (1+3i)$

D) $\pm (3-i)$

• A) 15

B) 25

C) - 25

D) None of these

• A) $\pm (b+ia)$

B) $\pm (a-ib)$

C) $\pm (b-ia)$

D) None of these

• A) $\pm (2+i)$

B) $\pm (2-i)$

C) $\pm (1-2i)$

D) $\pm (1+2i)$

• A) ${{x}^{2}}+{{y}^{2}}$

B) $\sqrt{{{x}^{2}}+{{y}^{2}}}$

C) $x+iy$

D) $x-iy$

• A) Infinite

B) 1

C) 2

D) None of these

• A) $\sqrt{2}\left( \cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4} \right)$

B) $\sqrt{2}\left( \cos \frac{\pi }{4}+i\sin \frac{\pi }{4} \right)$

C) $\left( \cos \frac{3\pi }{4}+i\sin \frac{3\pi }{4} \right)$

D) None of these

• A) ${{e}^{r\sin \theta }}$

B) ${{e}^{-r\sin \theta }}$

C) ${{e}^{-r\cos \theta }}$

D) ${{e}^{r\cos \theta }}$

• A) $\cos \frac{\pi }{2}+i\sin \frac{\pi }{2}$

B) $\cos \frac{\pi }{2}-i\sin \frac{\pi }{2}$

C) $\sin \frac{\pi }{2}+i\cos \frac{\pi }{2}$

D) None of these

• A) $\frac{\pi }{3}$

B) $-\frac{\pi }{3}$

C) $\frac{2\pi }{3}$

D) $-\frac{2\pi }{3}$

• A) $2\cos \theta$

B) $2\sin \theta$

C) $2\text{cosec}\theta$

D) $2\tan \theta$

• A) $\frac{1+\sqrt{3}i}{2}$

B) $\frac{1-\sqrt{3}i}{2}$

C) $\frac{-\sqrt{3}-i}{2}$

D) $\frac{\sqrt{3}-i}{2}$

• A) 1

B) 256

C) 0

D) ${{9}^{3}}$

• A) ${{e}^{\cos \theta }}[\cos (\sin \theta )]$

B) ${{e}^{\cos \theta }}[\cos (\cos \theta )]$

C) ${{e}^{\sin \theta }}[\sin (\cos \theta )]$

D) ${{e}^{\sin \theta }}[\sin (\sin \theta )]$

• A) $\sin \theta$

B) $-\sin \theta$

C) ${{e}^{\cos \theta }}$

D) ${{e}^{\sin \theta }}$

• A) $\cos \frac{\pi }{3}+i\,\sin \frac{\pi }{3}$

B) $\cos \frac{\pi }{2}+i\,\sin \frac{\pi }{2}$

C) $\sin \frac{\pi }{6}+i\,\cos \frac{\pi }{6}$

D) $\cos \frac{\pi }{6}+i\,\sin \frac{\pi }{6}$

• A) ${{2}^{20}}{{(-1+i\sqrt{3})}^{20}}$

B) ${{2}^{20}}{{(1-i\sqrt{3})}^{20}}$

C) ${{2}^{20}}{{(-1-i\sqrt{3})}^{20}}$

D) None of these

• A) 0

B) $\infty$

C) $\log 2$

D) $\log 4$

• A) ${{e}^{-\pi /4}}\cos \left( \frac{1}{2}\log 2 \right)$

B) $-{{e}^{-\pi /4}}\sin \left( \frac{1}{2}\log 2 \right)$

C) ${{e}^{\pi /4}}\cos \left( \frac{1}{2}\log 2 \right)$

D) ${{e}^{-\pi /4}}\sin \left( \frac{1}{2}\log 2 \right)$

• A) $\pi +2{{\tan }^{-1}}x$

B) $\pi -2{{\tan }^{-1}}x$

C) $-\pi +2{{\tan }^{-1}}x$

D) $-\pi -2{{\tan }^{-1}}x$

• A) -i

B) 1

C) -1

D) None of these

• A) ${{2}^{7}}$

B) ${{2}^{7}}i$

C) ${{2}^{14}}i$

D) $-{{2}^{7}}i$

E) $-{{2}^{14}}$