Results 1 to 4 of 4

Math Help - Finding r and the exact value

  1. #1
    Junior Member
    Joined
    Feb 2009
    Posts
    30

    Finding r and the exact value

    I have no idea how to do these problems on my review, can someone please explain how to do these.

    1. -2+5i= r(cosθ+isinθ), find θ accurate to 3 decimal places. Be sure your answer is in the correct quadrant.

    2. If θis an angle in the third quadrant and sinθ= -1/5 find the exact value of tan
    2θ. I did not rationalize the denominator.

    3. If 2+5i =
    r(cosθ+isinθ), find r.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Apr 2009
    Posts
    15
    There are formulae for these
    So if your complex number is a+bi,

    r=√(aČ+bČ)

    Now for θ you need to make sure you get your answer in the right quadrant.
    So draw your complex number on an argand diagram and see where it is.

    If it's in the 1st quadrant, eg. 2+5i, then θ = arctan(b/a)
    2nd quadrant, eg. -2+5i, then θ = pi - arctan(b/a)
    3rd quadrant, eg. -2-5i, then θ = arctan(b/a) - pi
    4th quadrant, eg. 2-5i, then θ = - arctan(b/a)

    I hope this helps.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    Posts
    30
    Ok, so if I got you correct then

    3. square root(29)

    1.
    Also for this one I looked up some stuff online but I think I got it wrong

    tan^(-1)(y/x)=5/2=68.2(rounded)
    180 -68=112
    Square root 29(cos(thata)+isin(thata)=5.39
    5.39(cos(112)+isin(112)=-2?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Apr 2009
    Posts
    15
    Quote Originally Posted by goldenroll View Post
    Ok, so if I got you correct then

    3. square root(29)

    1.
    Also for this one I looked up some stuff online but I think I got it wrong

    tan^(-1)(y/x)=5/2=68.2(rounded)
    180 -68=112
    Square root 29(cos(thata)+isin(thata)=5.39
    5.39(cos(112)+isin(112)=-2?
    Yup, Q3. is right

    For Q1. θ is usually calculated in radians, so you'll have to put your calculator into radians. You've got the right idea though.
    (I forgot to mention that when you're working out arctan(b/a), always take the positive of b and a. What you do with the quadrant thing will make sure the answer's right. You did that anyways though )

    So -2+5i is in the 2nd quadrant, so pi - arctan(5/2) = 1.951 to 3dp.

    You can check this: √29(cos(1.951)+ i sin(1.951)) = -1.998 + 5.001i
    (It's not exact because your theta was rounded)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding the exact value of sin 3
    Posted in the Trigonometry Forum
    Replies: 12
    Last Post: April 14th 2012, 02:25 AM
  2. finding the exact value..
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: April 26th 2010, 07:44 AM
  3. finding the exact value
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: December 30th 2009, 03:25 PM
  4. Finding the exact value using CAS
    Posted in the Calculators Forum
    Replies: 2
    Last Post: March 30th 2009, 02:58 AM
  5. Finding the exact value
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: June 10th 2008, 08:31 PM

Search Tags


/mathhelpforum @mathhelpforum