Argument of a random complex no. lying on given line segment.

[Ricky_15]

Homework Statement

In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options .

A) -3∏/4

B) ∏/4

C) 5∏/6

D) ∏/6

2. MY ATTEMPT AT THE SOLUTION

We get two points ( -3 , 5 ) & ( -5 , -3 ) => The line segment must intersect x - axis and lie in the 2nd and 3rd quadrant .
=> #z# lies on x-axis or 2nd or 3rd qudrant .

But , since there is no option ∏ , so z must be lying in 2nd or 3rd quadrant.

=> -3∏/4 or 5∏/6 should be the solution .

I can't proceed further from here so as to differentiate between the above two choices.

The answer in the book is : 5∏/6 .

 

[haruspex]

The set of choices is only defined as far as directions from the origin. So I would think the approach is to find the arguments of z1 and z2.

 

[LCKurtz]

How is your line situated with respect to the line $y = x$, which is where a $z$ with argument $-\frac{3\pi}{4}$ would be? Draw a graph.

 

[jk22]

You could also compute the argument : z=end-start and arg z or atan dy/dx

 

[BvU]

Hello Rick,

If you pick random points on the line between those two points on your drawing, the average postion of those points should end up where, do you think ? You calculated the intersection with the negative x-axis, but you should have calculated the midpoint of the line segment. The angle that is closest to the argument of that point is your best answer.

Oh, and: you did draw a graph, I hope ?

 

[SammyS]

Homework Statement

In the argand plane z lies on the line segment joining # z_1 = -3 + 5i # and # z_2 = -5 - 3i # . Find the most suitable answer from the following options .

A) -3π/4

B) π/4

C) 5π/6

D) π/6
...

Is that a complete statement of the problem - word for word?

If not, please give a complete statement of the problem - word for word. Also, if a portion of your question is in the thread title, please include it in the body of the thread as well.

 

[LCKurtz]

Anyone want to give odds on the OP ever returning to this thread?

 

[SammyS]

$\displaystyle \ \left(\frac{1}{e}\right)^\pi \$

 

[haruspex]

$\displaystyle \ \left(\frac{1}{e}\right)^\pi \$

That's completely irrational. Probably.

 

[Ricky_15]

Is that a complete statement of the problem - word for word?

If not, please give a complete statement of the problem - word for word. Also, if a portion of your question is in the thread title, please include it in the body of the thread as well.

I am extremely sorry . I was in a hurry . Thats not the complete question . The question asked for " find the suitable solution for arg(z) " .

 

[haruspex]

I am extremely sorry . I was in a hurry . Thats not the complete question . The question asked for " find the suitable solution for arg(z) " .

Have you tried my suggestion in post #2?

 

[Ricky_15]

Have you tried my suggestion in post #2?

Yup that solved it , but for that I needed a calculator to find tan inverse 3/5 & 5/3 .