Solve the equation $\left|z\right|=z+1+2i$ for $z$.

Important Questions on Complex Numbers and Quadratic Equations

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 12

If $|z+1|=z+2(1+i)$, then find $z$.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 13

If $\arg (z-1)=\arg (z+3i)$, then find $x-1:y$, where $z=x+iy$

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 14

Show that $\left|\frac{z-2}{z-3}\right|=2$ represents a circle. Find its center and radius.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 15

If $\frac{z-1}{z+1}$ is a purely imaginary number $(z\ne -1)$, then find the value of $\left|z\right|$.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 16

$z_1$ and $z_2$ are two complex numbers such that $\left|z_1\right|=\left|z_2\right|$ and $\arg \left(z_1\right)+\arg \left(z_2\right)=\pi$, then show that $z_1=-{\overline{z}}_2$.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 17

If $\left|z_1\right|=1\left(z_1\ne -1\right)$ and $z_2=\frac{z_1-1}{z_1+1}$, then show that the real part of $z_2$ is zero.

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 18

If $Z_1, Z_2$ and $Z_3, Z_4$ are two pairs of conjugate complex numbers, then find $arg\left(\frac{z_1}{z_4}\right)+\arg \left(\frac{z_2}{z_3}\right)$.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 19

If $\left|z_1\right|=\left|z_2\right|=\dots =\left|z_n\right|=1$, then show that $\left|z_1+z_2+z_3+\dots +z_n\right|=\left|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}+\dots +\frac{1}{z_n}\right|$.