# 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 .

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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.

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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

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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 ?

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## 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.

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

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

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##\displaystyle \ \left(\frac{1}{e}\right)^\pi \ ##
That's completely irrational. Probably.

Samy_A, Mentallic and SammyS
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) " .