Test: Geometry Of Complex Numbers - JEE MCQ

Test: Geometry Of Complex Numbers - JEE MCQ

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10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Geometry Of Complex Numbers

Test: Geometry Of Complex Numbers for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Geometry Of Complex Numbers questions and answers have been prepared according to the JEE exam syllabus.The Test: Geometry Of Complex Numbers MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Geometry Of Complex Numbers below.
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Test: Geometry Of Complex Numbers - Question 1

For a complex number x + iy, if x > 0 and y < 0 then the number lies in the.

Detailed Solution for Test: Geometry Of Complex Numbers - Question 1

When x > 0 & y < 0, the quadrant contains positive X-axis and negative Y-axis
Therefore, the point lies in the fourth quadrant.

Test: Geometry Of Complex Numbers - Question 2
Detailed Solution for Test: Geometry Of Complex Numbers - Question 2

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Test: Geometry Of Complex Numbers - Question 3

If |z1| = 4, |z2| = 4, then |z1 + z2 + 3 + 4i| is less than

Detailed Solution for Test: Geometry Of Complex Numbers - Question 3

Test: Geometry Of Complex Numbers - Question 4

If z is a complex number such that  is purely imaginary, then what is |z| equal to ?

Detailed Solution for Test: Geometry Of Complex Numbers - Question 4

Concept:
If a number ω = a + ib is purely imaginary, then

• a = 0
• and ω =

Calculation:
Given, z is a complex number such that is purely imaginary,
Let = a + ib, then a = 0
And

Test: Geometry Of Complex Numbers - Question 5

If A =  then the locus of the point P(x, y) in the cartesian plane is

Detailed Solution for Test: Geometry Of Complex Numbers - Question 5

z̅  = x - iy
Real Part of = Real Part of = Real Part of
⇒Real Part of

⇒ x2 - x - y2 + y = 2x2 + 2y2 - 4y + 2
⇒ x2 + 3y2 + x - 5y + 2 = 0
The above equation does not represent a circle or Straight line.
So No Option is Correct.
Option (2) is correct only when we use Z in place of Z̅ in the numerator of

Test: Geometry Of Complex Numbers - Question 6

A point z = P(x,y) lies on the negative direction of y axis, so amp(z) =

Detailed Solution for Test: Geometry Of Complex Numbers - Question 6

P(-x,-y) lies on the 3rd or 4th quadrant
So, according to the question, points lies in 3rd quadrant
i.e. 3(π/2)

Test: Geometry Of Complex Numbers - Question 7

The argument of the complex number -i

Detailed Solution for Test: Geometry Of Complex Numbers - Question 7

z = -i
Comlex number z is of the form x + iy
x = 0, y = -1
arg(z) = π − tan−1|y/x|
⇒ π − tan−1|-1/0|
= π - (π/2)
⇒  π - π/2
⇒ π/2

Test: Geometry Of Complex Numbers - Question 8

The modulas of the complex number -1 + √3i is

Detailed Solution for Test: Geometry Of Complex Numbers - Question 8

√(-1)2 + (√3)2

= 2

Test: Geometry Of Complex Numbers - Question 9

The argument of the complex number -1 – √3

Detailed Solution for Test: Geometry Of Complex Numbers - Question 9

z = a + ib
a = -1, b = -√3
(-1, -√3) lies in third quadrant.
Arg(z) = -π + tan-1(b/a)
= - π + tan-1(√3)
= - π + tan-1(tan π/3)
= - π + π/3
= -2π/3

Test: Geometry Of Complex Numbers - Question 10

The amplitude of a complex number is called the principal value amplitude if it lies between.

Detailed Solution for Test: Geometry Of Complex Numbers - Question 10

x = |z| cos θ and y = |z| sin θ satisfies infinite values of θ and for any infinite values of θ is the value of Arg z. Thus, for any unique value of θ that lies in the interval - π < θ ≤ π and satisfies the above equations x = |z| cos θ and y = |z| sin θ is known as the principal value of Arg z or Amp z and it is denoted as arg z or amp z.

We know that, cos (2nπ + θ) = cos θ and sin (2nπ + θ) = sin θ (where n = 0, ±1, ±2, ±3, .............), then we get,

Amp z = 2nπ + amp z where - π < amp z ≤ π

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