Solve Complex Numbers Homework: Arg (z) = pi/3

[missmerisha]

Homework Statement

If z = x + ( x+1) i, find the value of x for which Arg (z) = pi/3

Homework Equations

The Attempt at a Solution

( x+1/x) = pi/3
x = 3/( pi -3)

Answer: ( 3) ^(1/2) + 1 divided by 2

 

[e(ho0n3]

( x+1/x) = pi/3
x = 3/( pi -3)

Where did you get these equations from? Remember that $\arg z = \theta$ is equivalent to $z = |z|(\cos \theta + i \sin \theta)$.

 

[missmerisha]

I'm working out the arg of z in term of x
tan ( y/ x) = ( x+1)/ x = pi/3

 

[belliott4488]

I assume x is a real number, correct?

It might help you to draw the point z in the complex plane. What is the horizontal component of z? What is the vertical component? Where is the angle arg(z)? You should have a right triangle with one of the angles equal to pi/3.

Once you've drawn this, you can use what you know about this triangle to write the equation for x. (pi/3 rad = 30 deg, in case you forgot that.)

 

[belliott4488]

Oops - your second post came in while I was responding.

Be careful - arg(z) = pi/3 is the angle, so tan(y/x) = pi/3 is wrong.

(You've just got it backwards - recall how tan() is defined and you're there.)

 

[missmerisha]

so it's
tan ( pi/3 ) = ( x+ 1 / x)

 

[belliott4488]

isn't the equation just
tan ( (x+1)/x) = pi/3 ?

Nope. What kind of number goes into the argument of a trig function? (You're really close, you just need to remember the definition of the tan function a little better.)

 

[belliott4488]

so it's
tan ( pi/3 ) = ( x+ 1 / x)

We crossed messages again ...

Yes! tan(angle) = y/x, so now you can solve the equation you just wrote.

 

[missmerisha]

don't worry, I've got it. Thank you!

 

[e(ho0n3]

See my post.