The equation $z^3+iz-1=0, i=\sqrt{-1}$ has

Important Questions on Complex Numbers

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 7

If $a,b$ are complex numbers and one of the roots of the equation $x^2+ax+b=0$ is purely real whereas, the other root is purely imaginary, and ${\mathrm{a}}^2-{\overline{\mathrm{a}}}^2=kb$. Then $k$ is:

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 8

If $Z$ is a non-real complex number, then the minimum value of $\frac{\mathit{Im}{Z}^5}{{\mathit{Im}}^{5}Z}$ is

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 9

If $z_1, z_2, z_3$ are any three complex numbers on the argand plane, then $z_1\left(Im\left({\overline{z}}_2{z}_3\right)\right)+z_2\left(\mathrm{Im}\left({\overline{z}}_3{z}_1\right)\right)+z_3\left(\mathrm{Im}\left({\overline{z}}_1{z}_2\right)\right)$ is equal to

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 10

Complex numbers whose real and imaginary parts $x$ and $y$ are integers and satisfy the equation $3x^2-\left|xy\right|-2y^2+7=0$.

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 11

For a complex number $z$, if all the three roots of $a{z}^3+b{z}^2+cz+d=0$ have negative real parts $(a, b, c\in R)$, then 

HARD

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 12

Suppose three real numbers $a, b, c$ are in $\mathrm{G}.\mathrm{P}.$ and $z=\frac{a+ib}{c-ib}$. Then,

EASY

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 1

The modulus and amplitude of $\frac{1+2i}{1-(1-i{)}^2}$ are

MEDIUM

JEE Main

IMPORTANT

Chapterwise/Topicwise Daily Practice Problems (DPP) Algebra JEE Main & Advanced>Chapter 3 - Complex Numbers>DPP>Q 2

The argument of $\left(z-a\right)\left(\overline{z}-b\right)$ is equal to that of $\frac{\left(\sqrt{3}+i\right)\left(1+\sqrt{3}i\right)}{1+i}$  where  $a,b$ are real numbers. If the locus of $z$ in the Argand diagram is a circle with its centre at $\frac{\left(3+i\right)}{2}$, then the ordered pair $\left(a,b\right)$ is