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If arg(z+a) = pi//6 and arg(z-a) = 2 pi/...

If `arg(z+a) = pi//6 and arg(z-a) = 2 pi//3 (a in R^(+))`, then

A

`|z| = a`

B

`|z|=2a`

C

`arg(z) = (pi)/(2)`

D

`arg(z) = (pi)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A, D
Refer to figure, z lie on the point of intersection of the rays from A and B . `/_ ACB` is a right angle and OBC is an equilateral triangle. Hence,
`OC = a rArr z=a (cos.(pi)/(3) + i sin.(pi)/(3))`
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CENGAGE-COMPLEX NUMBERS-Exercise (Multiple)
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  3. If arg(z+a) = pi//6 and arg(z-a) = 2 pi//3 (a in R^(+)), then

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  5. If |z-1|=1, then

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  6. If z(1) = 5 + 12i and |z(2)| = 4, then

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  7. Let z(1),z(2),z(3) be the three nonzero comple numbers such that z(2)...

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  8. z(1) and z(2) are the roots of the equaiton z^(2) -az + b=0 where ...

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  9. If |(z-z(1))//(z-z(2))| = 3, where z(1) and z(2) are fixed complex ...

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  10. If z=x+i y , then he equation |(2z-i)//(z+1)|=m represents a circle, t...

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  11. System of equaitons |z+3|-|z-3| = 6 and |z-4|=r where r in R^(+) has

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  12. Let the equaiton of a ray be |z-2|-|z-1-i| = sqrt(2). If the is stri...

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  15. Let S = { z: x = x+ iy, y ge 0,|z-z(0)| le 1}, where |z(0)|= |z(0) - o...

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  16. If P andn Q are represented by the complex numbers z(1) and z(2) such...

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  17. Loucus of complex number satifying are arg[(z-5+4i)//(z+3-2i)] = - pi...

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  19. If n is a natural number gt 2, such that z^(n) = (z+1)^(n), then

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