Complex Numbers Questions

MathematicsComplex Numbers105 Questions Found

MathematicsGeometrical Applications of Complex NumbersJEE Main 2012Moderate

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If $z \neq = 1$ and $\frac{z ^{2}}{z - 1}$ is real, then the point represented by the complex number $z$ lies

(A)

either on the real axis or on a circle passing through the origin.

(B)

on a circle with centre at the origin

(C)

either on the real axis or on a circle not passing through the origin.

(D)

on the imaginary axis.

Answer:A

MathematicsConjugate and ModulusJEE Main 2013Easy

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If $z$ is a complex number of unit modulus and argument $θ$ , then $a r g (\frac{1 + z}{1 + z ˉ})$ equals

(A)

- θ

(B)

π /2 - θ

(C)

θ

(D)

π - θ

Answer:C

MathematicsGeometrical Applications of Complex NumbersJEE Main 2014Easy

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If $z$ is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $∣ z + 1/2∣$

(A)

is strictly greater than 5/2

(B)

is strictly greater than 3/2 but less than 5/2

(C)

is equal to 5/2

(D)

lie in the interval (1, 2)

Answer:B

MathematicsConjugate and ModulusJEE Main 2015Moderate

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A complex number $z$ is said to be unimodular if $∣ z ∣ = 1$ . Suppose $z_{1}$ and $z_{2}$ are complex numbers such that $\frac{z _{1} - 2 z _{2}}{2 - z _{1} z ˉ _{2}}$ is unimodular and $z_{2}$ is not unimodular. Then the point $z_{1}$ lies on a

(A)

circle of radius 2.

(B)

circle of radius

2

(C)

straight line parallel to x-axis

(D)

straight line parallel to y-axis.

Answer:A

MathematicsAlgebraic Operations on Complex NumbersJEE Main 2016Easy

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A value of $θ$ for which $\frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}$ is purely imaginary, is

(A)

sin^{- 1} (3 /4)

(B)

sin^{- 1} (1/ 3)

(C)

π /3

(D)

π /6

Answer:B

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If z is a complex number of unit modulus and argument θ, then arg(1+zˉ1+z​) equals

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If z is a complex number such that ∣z∣≥2, then the minimum value of ∣z+1/2∣

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.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } If z is a complex number such that ∣z∣≥2, then the minimum value of ∣z+1/2∣

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If $z \neq = 1$ and $\frac{z ^{2}}{z - 1}$ is real, then the point represented by the complex number $z$ lies

If $z$ is a complex number of unit modulus and argument $θ$ , then $a r g (\frac{1 + z}{1 + z ˉ})$ equals

If $z$ is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $∣ z + 1/2∣$

A value of $θ$ for which $\frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}$ is purely imaginary, is

If $z \neq = 1$ and $\frac{z ^{2}}{z - 1}$ is real, then the point represented by the complex number $z$ lies

If $z$ is a complex number of unit modulus and argument $θ$ , then $a r g (\frac{1 + z}{1 + z ˉ})$ equals

If $z$ is a complex number such that $∣ z ∣ \geq 2$ , then the minimum value of $∣ z + 1/2∣$

A value of $θ$ for which $\frac{2 + 3 i s i n θ}{1 - 2 i s i n θ}$ is purely imaginary, is