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    How do I go from

    1 / (-8 - 6i)

    to

    (-8 + 6i) / 100


    Also, If I had to work out the real and imaginary parts of that, and I left it as 1/(-8) and 1/(-6), would I still get all the marks?
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      (Original post by claret_n_blue)
      How do I go from

      1 / (-8 - 6i)

      to

      (-8 + 6i) / 100
      Are you familiar with the idea of the complex conjugate?

      (Original post by claret_n_blue)
      Also, If I had to work out the real and imaginary parts of that, and I left it as 1/(-8) and 1/(-6), would I still get all the marks?
      No, because that's wrong. You can't split fractions up like you are trying to do.
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      (Original post by Kolya)
      Are you familiar with the idea of the complex conjugate?
      Yes I am. So is that simply the conjugate of the other? Why does it go above 100?

      (Original post by Kolya)
      No, because that's wrong. You can't split fractions up like you are trying to do.
      Oh yeah, silly me lol.
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      (Original post by claret_n_blue)
      Yes I am. So is that simply the conjugate of the other? Why does it go above 100?



      Oh yeah, silly me lol.
      multiply the original (top and bottom) by the conjugate and simplify
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      (Original post by hey_its_nay)
      multiply the original (top and bottom) by the conjugate and simplify
      Why do you do that? Is it simply because that's the method to work out the real and imaginary parts when you are in a situation like this?
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      (Original post by claret_n_blue)
      Why do you do that? Is it simply because that's the method to work out the real and imaginary parts when you are in a situation like this?
      If z=a+bi then \bar{z} = a-bi, and so z \bar{z} = a^2+b^2 = |z|^2.

      But then, \dfrac{1}{z} = \dfrac{1}{z} \times \dfrac{\bar{z}}{\bar{z}} = \dfrac{\bar{z}}{|z|^2}.

      This is the rule they've used. That is, that \dfrac{1}{a+bi} = \dfrac{a-bi}{a^2+b^2}. This then allows you to separate the real and imaginary part. You wouldn't get any marks for the answer you gave, because it's not right.
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      (Original post by claret_n_blue)
      Why do you do that? Is it simply because that's the method to work out the real and imaginary parts when you are in a situation like this?
      it removes imaginary parts from the denominator
      read the post above... they explain it very well
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      64+36 = 100
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      1/(-8 - 6i)
      z= -8 - 6i
      z*= -8 + 6i (z* denotes the complex conjugate)

      1/(-8 - 6i) x (-8 + 6i)/(-8 + 6i)
      (-8 + 6i)/[(-8 - 6i)(-8 + 6i)]
      (-8 + 6i)/(64 -48i +48i +36)
      (-8 + 6i)/100
     
     
     
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