Results 1 to 5 of 5

Math Help - Multiplying CIS

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    8

    Multiplying CIS

    Can someone help me here?
    "The product of 4(cos30 + i sin30) and 3(cos90 + i sin90) is equal to..."

    The answer is 6(-1 + i rad(3)) apparently but I don't know where that came from.

    I can never remember how to do these for some reason...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28
    Do you mean?

    4(\cos(30) + i \sin(30)) \times 3(\cos(90) + i \sin(90))

    4\left(\frac{\sqrt{3}}{2} + i \frac{1}{2}\right) \times 3( 0+ i\times 1)

    12\left(\frac{\sqrt{3}}{2} + i \frac{1}{2}\right) \times i

    12\left(\frac{\sqrt{3}}{2}i + i^2 \frac{1}{2}\right)

    12\left(\frac{\sqrt{3}}{2}i -\frac{1}{2}\right)

    6\sqrt{3}i -6
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Aug 2008
    Posts
    8
    Yes thank you!

    I'm wondering...is it possible to state that answer in cis form?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2009
    Posts
    49
    of course - all complex numbers can be stated in cis form
    just find the mod and angle in the complex graph
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,326
    Thanks
    1298
    That is surely the hard way! The whole point of the "polar form", r cis(\theta) (also written r(cos(\theta)+ i sin(\theta) and even re^{i\theta}), is that
    (r_1 cis(\theta_1))(r_2 cis(\theta_2))= (r_1r_2) cis(\theta_1+ \theta_2).

    Here, (4 cis(30))(3 cis(90))= (12) cis(120)= 12(cos(120)+ i sin(120)). Since the numbers were given in "cis" form, I would leave the answer in that form. If you like, cos(120)= -\frac{1}{2} and sin(120)= \frac{\sqrt{3}}{2} so 12 cis(120)= -6+ 6i\sqrt{3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Multiplying matrices what is W?
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 10th 2010, 08:46 PM
  2. Multiplying in GF(2)
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: February 8th 2010, 10:20 AM
  3. Multiplying with indices
    Posted in the Algebra Forum
    Replies: 5
    Last Post: October 2nd 2009, 01:25 AM
  4. multiplying negatives
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 8th 2009, 02:02 PM
  5. Multiplying a fraction by 100
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 5th 2008, 02:30 AM

Search Tags


/mathhelpforum @mathhelpforum