Mathematics Multiple Choice Questions on “Argand Plane and Polar Representation”.
1. Which axis is known as real axis in argand plane?
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: a
Clarification: The plane having a complex number assigned to each of its point is called the
complex plane or the Argand plane. When (x + y i) is plotted in argand plane, x-axis is real axis.
2. Which axis is known as imaginary axis in argand plane?
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: b
Clarification: The plane having a complex number assigned to each of its point is called the
complex plane or the Argand plane. When (x + y i) is plotted in argand plane, y-axis is imaginary axis.
3. 2+i0 is point on ______________
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: a
Clarification: Since imaginary part of complex number is zero. So, it is plotted on real axis i.e. x-axis.
2+i0 is point on x-axis.
4. 6i is point on ____________________
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: b
Clarification: Since real part of complex number is zero. So, it is plotted on imaginary axis i.e. y-axis.
6i is point on y-axis.
5. (sqrt{x^2+y^2}) distance of point representing complex number x+y i from origin.
a) True
b) False
Answer: a
Clarification: Since complex number x + y i is represented by (x, y) on argand plane, distance of point (x, y) from origin is (sqrt{x^2+y^2}).
6. Find mirror image of point representing x+i y on real axis.
a) (x, y)
b) (-x, -y)
c) (-x, y)
d) (x, -y)
Answer: d
Clarification: Mirror image of point (x, y) on real axis is (x, -y).
Since real axis is acting as mirror x-coordinate remains same whereas y-coordinate gets inverted.
So, (x, -y) is mirror image of (x, y) on real axis.
7. Find mirror image of point representing x+i y on imaginary axis.
a) (x, y)
b) (-x, -y)
c) (-x, y)
d) (x, -y)
Answer: c
Clarification: Mirror image of point (x, y) on imaginary axis is (-x, y).
Since imaginary axis is acting as mirror y-coordinate remains same whereas x-coordinate gets inverted. So, (-x, y) is mirror image of (x, y) on imaginary axis.
8. If P and Q are conjugate complex numbers then their points on argand plane are mirror image on __________________
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: a
Clarification: Conjugate complex numbers means their real part is same and imaginary part is inverted i.e. same x part and opposite imaginary part. So, they are mirror image on real axis i.e. x-axis.
9. In polar representation of a complex number (r, 2π) lies on ____________
a) x-axis
b) y-axis
c) z-axis
d) any axis
Answer: a
Clarification: To convert polar representation (r, θ) into argand plane (x, y), substitute x = r cos θ and y = r sin θ.
x = r cos 2π = r and y = r sin 2π = 0.
Argand plane representation is (r, 0). Since imaginary part is zero, so it lies on real axis i.e. x-axis.
10. In polar representation of a complex number (r, π/2) lies on ____________
a) x-axis
b) y-axis
c) z-axis
d) any axis