Home
Class 12
MATHS
z(1), z(2) are two distinct points in co...

`z_(1)`, `z_(2)` are two distinct points in complex plane such that `2|z_(1)|=3|z_(2)|` and `z in C` be any point `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))` such that

A

`-1 le Re z le 1`

B

`-2 le Re z le 2`

C

`-3 le Re z le 3`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `z=(2z_(1))/(3z_(2))+(3z_(2))/(2z_(1))`
`=(2)/(3)(|z_(1)|)/(|z_(2)|)e^(i(theta_(1)-theta_(2)))+(3)/(2)(|z_(2)|)/(|z_(1)|)e^(i(theta_(2)-theta_(1)))`
`=e^(i(theta_(1)-theta_(2)))+e^(i(theta_(2)-theta_(1)))=2cos(theta_(1)-theta_(2))=2cosalpha`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE ENGLISH|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE ENGLISH|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|101 Videos

Similar Questions

Explore conceptually related problems

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Let z_(1) and z_(2) be any two non-zero complex numbers such that 3|z_(1)|=2|z_(2)|. "If "z=(3z_(1))/(2z_(2)) + (2z_(2))/(3z_(1)) , then

If z_(1) and z_(2) are two complex numbers such that |(z_(1)-z_(2))/(z_(1)+z_(2))|=1 , then

If z_(1) and z_(2) are two complex numbers such that |z_(1)|= |z_(2)| , then is it necessary that z_(1) = z_(2)

Let four points z_(1),z_(2),z_(3),z_(4) be in complex plane such that |z_(2)|= 1, |z_(1)|leq 1 and |z_(3)| le 1 . If z_(3) = (z_(2)(z_(1)-z_(4)))/(barz_(1)z_(4)-1) , then |z_(4)| can be (a) 2 (b) 2/5 (c) 1/3 (d) 5/2

Let z_(1),z_(2) and z_(3) be three complex number such that |z_(1)-1|= |z_(2) - 1| = |z_(3) -1| and arg ((z_(3) - z_(1))/(z_(2) -z_(1))) = (pi)/(6) then prove that z_(2)^(3) + z_(3)^(3) + 1 = z_(2) + z_(3) + z_(2)z_(3) .

If z_(1), z_(2) and z_(3) are the vertices of a triangle in the argand plane such that |z_(1)-z_(2)|=|z_(1)-z_(3)| , then |arg((2z_(1)-z_(2)-z_(3))/(z_(3)-z_(2)))| is

If z_(1), z_(2), z_(3) are 3 distinct complex such that (3)/(|z_(1)-z_(2)|)=(5)/(|z_(2)-z_(3)|)=(7)/(|z_(3)-z_(1)|) , then the value of (9barz_(3))/(z_(1)-z_(2))+(25barz_(1))/(z_(2)-z_(3))+(49barz_(2))/(z_(3)-z_(1)) is equal to

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)

If z_(1),z_(2),z_(3) are three complex numbers, such that |z_(1)|=|z_(2)|=|z_(3)|=1 & z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=0 then |z_(1)^(3)+z_(2)^(3)+z_(3)^(3)| is equal to _______. (not equal to 1)