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Pre-exam. algebra questions.

  1. Jan 19, 2005 #1
    1) Sketch the regions in the Argand diagram given by:

    |z+i| < |z-3|

    this means the distance from z to 3 is greater than the distance from z to i? would I then just draw two lines on the argand diagram, shading the lower region and not including the boundary? havent had a problem with these questions through term, guess im just a bit burned out and need to make sure. :uhh:

    2) Find the modulus and the argument of:
    1+ cosx + isinx

    does this involve changing the angle to x/2 and using trig expansions?

  2. jcsd
  3. Jan 19, 2005 #2
    In this case it is useful to express these complex numbers as z = a+ib and then calculate the modulus. You know that a is on the x-axis and y is on the imaginary y-axis...

    This oughtta help you out...i hope :biggrin:

    For example : Z + i = a + (b + 1)i

    Write out the inequality and look at a and b as the x and y coordinates of some first order inequality that you will need to solve... I tried it like this and it worked
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