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.
No comments:
Post a Comment