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JEE • MATHEMATICS • COMPLEX NUMBERS

Complex numbers practice · Easy

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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Showing 601-612 of 612 questions

601 Easy

601 of 612

Analyzing +4 | -1

Let

z

and

\omega

be complex numbers. If

\operatorname{Re}(z)=|z-2|

\operatorname{Re}(\omega)=|\omega-2|

and

\arg (z-\omega)=\frac{\pi}{3}

, the value of

\operatorname{Im}(z+\omega)

View answer and explanation

Correct option: D

\frac{4}{\sqrt{3}}

Option D (

\frac{4}{\sqrt{3}}

) is correct because by using parametric form of z and omega, and given argument, the imaginary part of z+omega can be found.

602 Easy

602 of 612

Application +4 | -1

Let

\left(-2-\frac{1}{3} \mathrm{i}\right)^3=\frac{\mathrm{x}+\mathrm{iy}}{27}(\mathrm{i}=\sqrt{-1})

, where

\mathrm{x}

and

y

are real numbers, then

y-x

equals :

View answer and explanation

Correct option: D

Option D (91) is correct because expanding the complex number expression and then calculating y - x results in 91.

603 Easy

603 of 612

Application +4 | -1

If the cube roots of unity are

1,\;\omega ,\;{\omega ^2}

, then the roots of the equation

{\left( {x - 2} \right)^3} + 27 = 0

are

View answer and explanation

Correct option: D

- 1,\;2 - 3\omega ,\;2 - 3{\omega ^2}

The correct answer is D (

- 1,\;2 - 3\omega ,\;2 - 3{\omega ^2}

) because it represents the solutions obtained by solving the given cubic equation using the properties of cube roots of unity.

604 Easy

604 of 612

Understanding +4 | -1

The values of

(16)^{1 / 4}

are

View answer and explanation

Correct option: A

\pm 2, \pm 2 i

Option A is correct because the fourth roots of 16 are

\pm 2

and

\pm 2i

605 Easy

605 of 612

Application +4 | -1

x

is an integer satisfying

{x^2} - 6x + 5 \le 0

and

{x^2} - 2x > 0,

then the number of positive values of

x

, is

View answer and explanation

Correct option: A

Option A (3) is correct because the integer values of x that satisfy both inequalities are 3, 4, and 5, resulting in 3 positive values.

606 Easy

606 of 612

Application +4 | -1

The value of

\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}

is :

View answer and explanation

Correct option: C

-2^{15} i

Option C (-2¹⁵ i) is correct because it is obtained by converting the complex numbers to polar form, simplifying the expression, and applying De Moivre's theorem.

607 Easy

607 of 612

Analyzing +4 | -1

Let

z=x+i y

be a complex number, where

x

and

y

are integers and

i=\sqrt{-1}

. Then, the area of the rectangle whose vertices are the roots of the equation

z \bar{z}^3+\bar{z} z^3=350

, is

View answer and explanation

Correct option: A

Option A (48) is correct because solving the equation leads to integer values for x and y, allowing calculation of the rectangle's area.

608 Easy

608 of 612

Analyzing +4 | -1

Let

z = x + iy

be a complex number where

x

and

y

are integers. Then the area of the rectangle whose vertices are the roots of the equation

z{z^{ - 3}} + \bar z{z^3} = 350

View answer and explanation

Correct option: A

Option D (48) is correct because the area of the rectangle formed by the roots is calculated as 8 * 6 = 48.

609 Easy

609 of 612

Application +4 | -1

\alpha

and

\beta

are the roots of the equation

x^2-x+1=0

\alpha^{2009}+\beta^{2009}

is equal to

View answer and explanation

Correct option: B

Option B (1) is correct because the expression simplifies to 1 using the properties of the roots of the given quadratic equation.

610 Easy

610 of 612

Application +4 | -1

In which quadrant of the complex plane, the point

\frac{{1 + 2i}}{{1 - i}}

lies?

View answer and explanation

Correct option: C

Second

Option C (Second) is correct because the simplified form of the complex number has a negative real part and a positive imaginary part.

611 Easy

611 of 612

Application +4 | -1

x, y, a, b \in \mathbf{R}, a \neq 0

and

(a+i b)(x+i y)=\left(a^2+b^2\right) i

, then

(x, y)

equals

View answer and explanation

Correct option: D

(b, a)

Option D (

(b, a)

) is correct because it is found by equating the real and imaginary parts after dividing both sides by (a+ib).

612 Easy

612 of 612

Application +4 | -1

Let

z,w

be complex numbers such that

\bar z + \overline {iw} = 0

and

\mathrm{\;arg}\left( {zw} \right) = \pi

. Then

\arg \left( z \right)

equals

View answer and explanation

Correct option: C

\frac{{3\pi }}{4}

Option C (

\frac{{3\pi }}{4}

) is correct because using the given conditions,

\arg(z)

can be found by relating

\arg(zw)

\arg(z)

and using the property

\arg(-i) = -\frac{\pi}{2}

Revision notes and key takeaways

Review COMPLEX NUMBERS in your textbook or class notes, then use this set to check your understanding.

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