WB JEE 2023 | Complex Numbers Question 20 | Mathematics

WB JEE 2023

MCQ (More than One Correct Answer)

-0

If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}} \right| = 1$$, then $${{{z_1}} \over {{z_2}}}$$ may be

real positive

real negative

zero

purely imaginary

WB JEE 2022

MCQ (More than One Correct Answer)

-0

Let z₁ and z₂ be two non-zero complex numbers. Then

Principal value of arg(z₁z₂) may not be equal to Principal value of argz₁ + Principal value of arg z₂

Principal value of arg(z₁z₂) = Principal value of argz₁ + Principal value of arg z₂

Principal value of arg(z₁/z₂) = Principal value of argz₁ $$-$$ Principal value of arg z₂

Principal value of arg(z₁/z₂) may not be argz₁ $$-$$ arg z₂

WB JEE 2021

MCQ (More than One Correct Answer)

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If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equal to

$$\sqrt 2 (1 + i)$$

$$\sqrt 2 (1 - i)$$

$$\sqrt 2 ( - 1 + i)$$

$$\sqrt 2 ( - 1 - i)$$

WB JEE 2019

MCQ (More than One Correct Answer)

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If $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta $$ will be (when I : Set of integers)

$$(2n + 1){\pi \over 2},n \in I$$

$${{3n\pi } \over 2},n \in I$$

$$n\pi ,n \in I$$

$$2n\pi ,n \in I$$

WB JEE Subjects