New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Complex Numbers question

2022 · 24 Jun · Shift 2 · Q37

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Complex Numbers
2022 · 24 Jun · Shift 2 · Q37

Complex Numbers question

2022 · 24 Jun · Shift 2 · Q37

JEE MainMathematicsComplex NumbersNumerical+4 / −1

Let S = {z

\in

C : |z

-

3|

\le

1 and z(4 + 3i) +

\overline z

(4

-

3i)

\le

24}. If

\alpha

+ i

\beta

is the point in S which is closest to 4i, then 25(

\alpha

+

\beta

) is equal to

\underline{\hspace{2cm}}

.

Numerical answer

More from Complex Numbers

For $n \in N$ , let $S_{n} = {z \in C : ∣ z - 3 + 2 i ∣ = \frac{n}{4}}$ and $T_{n} = {z \in C : ∣ z - 2 + 3 i ∣ = \frac{1}{n}}$ . Then the number…2022 · MCQ
For $z \in C$ if the minimum value of $(∣ z - 32 ∣ + ∣ z - p 2 i ∣)$ is $52$ , then a value Question: of $p$ is .2022 · MCQ
Let a circle C in complex plane pass through the points $z_{1} = 3 + 4 i$ , $z_{2} = 4 + 3 i$ and $z_{3} = 5 i$ . If $z (e z_{1})$ is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then $a r g (z)$ …2022 · MCQ
Let z1 and z2 be two complex numbers such that $\overline{z}_{1} = i \overline{z}_{2}$ and $ar g (\frac{z _{1}}{z _{2}}) = π$ . Then :2022 · MCQ
Let O be the origin and A be the point $z_{1} = 1 + 2 i$ . If B is the point $z_{2}$ , $Re o l imi t s (z_{2}) < 0$ , such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT…2022 · MCQ
If $z = x + i y$ satisfies $∣ z ∣ - 2 = 0$ and $∣ z - i ∣ - ∣ z + 5 i ∣ = 0$ , then :2022 · MCQ
Let $A = {z \in C : \frac{z + 1}{z - 1} < 1}$ and $B = {z \in C : ar g (\frac{z - 1}{z + 1}) = \frac{2 π}{3}}$ . Then A $\cap$ B is :2022 · MCQ
If $z^{2} + z + 1 = 0$ , $z \in C$ , then $n = 1 \sum 15 (z^{n} + (- 1)^{n} \frac{1}{z ^{n}})^{2}$ is equal to .2022 · Numerical