KC Sinha Mathematics Solution Class 11 Chapter 11 Complex Numbers Exercise 11.4

 Exercise 11.4

Page no 11.60

Question 1

Plot the following numbers and their complex conjugates on a complex number plane and find their absolute values :

(i) $4-3 i$

(ii) 1

(iii) $i$

(iv) $-\frac{4}{3} i$

(v) $\sqrt{-3}$

(vi) $\frac{\sqrt{3}}{2}+\frac{i}{2}$

Question 2

Plot all the complex number in the complex number plane whose absolute value is 5 

Question 3

Show that the points representing the complex number 3$+4 i, 8-6 i$ and 13+9i are the vertices of a right angled triangle.

Question 4

Prove that the points representing the $4+3 i, 6+4i , 5+6 i, 3+5 i$ are the vertices of a square.

Page no 11.61

Question 5

Prove that the points representing the complex numbers $3+2 i, 6+3 i, 7+6 i$ and $4+5 i$ are the vertices of a parallelogram. Is it a rectangle ?

Question 6

A variable complex number $z=x+i y$ is such that arg $\left(\frac{z-1}{z+1}\right)=\frac{\pi}{2}$, show that $x^{2}+y^{2}-1=0$

Question 7

Find the locus of point $z$ in the Argand plane if $\frac{z-1}{z+1}$ is purely imaginary.

Question 8

If the point representing $z$ in the Argand plane be equidistant from points $2+i$ and $1-2 i$, prove that $x+3 y=0$.

Question 9

Show that the complex number $z=x+i y$ satisfying the equation $\left|\frac{z-5 i}{z+5 i}\right|=1$ lies on the $x$-axis.