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Cartesian , Polar and Exponential Form . Help needed thanks .

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data

    how can i convert this : - 2 (cos pai / 4 + i sin pai / 4 ) to Cartesian , Polar and Exponential form ?


    2. Relevant equations

    z = ( a + i b)

    3. The attempt at a solution

    r= -2
    tan inverse = pai/4 / pai/4
    ??

    Thank you very much for helping me out
     
  2. jcsd
  3. Sep 28, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    It is already almost in "polar form". If you did not see that immediately, you need to review the definitions. The only reason it is not already in polar form is because the "r" in "[itex]r (cos(\theta)+ i sin(\theta))[/itex]" cannot be negative. Draw the line with [itex]\theta= \pi/4[/itex] and go backwards: [itex]-2(cos(\theta)+ i sin(\theta))= 2(cos(\theta+ \pi)+ i sin(\theta+ \pi)[/itex]

    On thing you should know is that the "r" in a polar
    To change to "Cartesian form", just evaluate the functions. What is [itex]cos(\pi/4)[/itex]? What is [itex]sin(-\pi/4)[/itex]? What are [itex]-2 cos(\pi/4)[/itex] and [itex]-2 sin(\pi/4)[/itex]?

    The "exponential form" of [itex]r(cos(\theta)+ i sin(\theta))[/itex] is [itex]r e^{i\theta}[/itex]. Again, r cannnot be negative.
     
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