Home
Class 12
MATHS
Suppose two complex numbers z=a+ib, w=c+...

Suppose two complex numbers `z=a+ib`, `w=c+id` satisfy the equation `(z+w)/(z)=(w)/(z+w)`. Then

A

both `a` and `c` are zeros

B

both `b` and `d` are zeros

C

both `b` and `d` must be non zeros

D

at least one of `b` and `d` is non zero

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `(z+w)^(2)=zw`
`impliesz^(2)+zw+w^(2)=0`
Let `(z)/(w)=timplies(z)/(w)=(-1+-sqrt(3)i)/(2)`
`argz-argw=(2pi)/(3)` or `argz-argw=-(2pi)/(3)`
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|11 Videos

  • COMPLEX NUMBERS

    CENGAGE PUBLICATION|Exercise Matching Column|1 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

Similar Questions

Explore conceptually related problems

The complex number z satisfying the equation |z-i|=|z+1|=1 is

The complex numbers z is simultaneously satisfy the equations abs(z-12)/abs(z-8i)=5/3,abs(z-4)/abs(z-8)=1 then the Re(z) is

Number of imaginary complex numbers satisfying the equation, z^2=bar(z)2^(1-|z|) is

If z and w are two complex numbers simultaneously satisfying the equations, z^3+w^5=0 and z^2 . overlinew^4 = 1, then

If the complex number z satisfies the equations |z-12|/|z-8i|=(5)/(3) and |z-4|/|z-8| =1, "find" z.

All complex numbers 'z' which satisfy the relation |z-|z+1||=|z+|z-1|| on the complex plane lie on the

Find the amplitude of the complex number z=a-ib .

Find the complex number satisfying system of equation z^(3)=-((omega))^(7) and z^(5).omega^(11)=1

The maximum value of |z| when the complex number z satisfies the condition |z+(2)/(z)|=2 is -

Find the complex number omega satisfying the equation z^3=8i and lying in the second quadrant on the complex plane.