JEE MAINS PRACTICE · Mathematics
Complex Numbers
462 practice questions for JEE Mains Practice — 241 easy · 198 medium · 23 hard. Every question is graded instantly with a step-by-step solution when you miss it.
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MCQ
Area of the triangle in the argand diagram formed by the complex numbers $z, i z, z+i z$, where $z=x+i y$ is
MCQ
The complex number $z=x+i y$ which satisfy the equation $\left|\frac{z-5 i}{z+5 i}\right|=1$, lie on
MCQ
If $\omega$ is a cube root of unity, then $\left(1+\omega-\omega^2\right)\left(1-\omega+\omega^2\right)$ is
MCQ
If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then the value of $\cos 3 \alpha+\cos 3 \beta+\cos 3 \gamma$ is
MCQ
If $x_n=\cos \frac{\pi}{3^n}+i \sin \frac{\pi}{3^n}$, then $x_1 \cdot x_2 \cdot x_3 \ldots$ is equal to
MCQ
If $z=\frac{-2}{1+\sqrt{3} i}$, then the value of $\arg (z)$ is
MCQ
If $n_1, n_2$ are positive integers, then $(1+i)^{n_1}+\left(1+i^3\right)^{n_1}+\left(1+i^5\right)^{n_2}+\left(1+i^7\right)^{n_2}$ is a real number if and only if
MCQ
If $\frac{(3-i)^2}{2+i}=A+i B$, where $A$ and $B$ are real numbers, then $A$ and $B$ are equal to
MCQ
If $Z=i \log (2-\sqrt{3})$, then the value of $\cos Z$ will be
MCQ
If $(\sqrt{3}-i)^{50}=2^{48}(x-i y)$, then $x^2+y^2$ is equal to
MCQ
$A+i B \text { form of } \frac{(\cos x+i \sin x)(\cos y+i \sin y)}{(\cot u+i)(1+i \tan v)}$is
MCQ
If $z=x+i y, z^{1 / 3}=a-i b$, then $\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)$, where $k$ is equal to: