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Math Help - Help with Complex Numbers

  1. #1
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    Help with Complex Numbers

    1.Find the product of Help with Complex Numbers-codecogseqn-3-.gif and Help with Complex Numbers-codecogseqn-4-.gif

    Help with Complex Numbers-codecogseqn-6-.gif
    Help with Complex Numbers-codecogseqn-7-.gif
    Help with Complex Numbers-codecogseqn-8-.gif
    Are those steps right so far? If so, how do I solve the rest?

    2.If Help with Complex Numbers-codecogseqn-13-.gif and Help with Complex Numbers-codecogseqn-10-.gif find Help with Complex Numbers-codecogseqn-11-.gif

    I got the answer 2e^(2pi/8)i

    But the correct answer is 2+i sq.rt2
    How do I get that answer?
    Attached Thumbnails Attached Thumbnails Help with Complex Numbers-codecogseqn-5-.gif   Help with Complex Numbers-codecogseqn-9-.gif  
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  2. #2
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    Re: Help with Complex Numbers

    Quote Originally Posted by INeedOfHelp View Post
    1.Find the product of Click image for larger version. 

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    Are those steps right so far? If so, how do I solve the rest?

    2.If Click image for larger version. 

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    I got the answer 2e^(2pi/8)i

    But the correct answer is 2+i sq.rt2
    How do I get that answer?

    I find your posting almost impossible to read. Why not learn LaTex?

    Given any complex number, it is true z\cdot\overline{z}=|z|^2.
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  3. #3
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    Re: Help with Complex Numbers

    Quote Originally Posted by INeedOfHelp View Post
    1.Find the product of Click image for larger version. 

Name:	CodeCogsEqn(3).gif 
Views:	1 
Size:	1.8 KB 
ID:	26086 and Click image for larger version. 

Name:	CodeCogsEqn(4).gif 
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ID:	26087

    Click image for larger version. 

Name:	CodeCogsEqn(6).gif 
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ID:	26089
    Click image for larger version. 

Name:	CodeCogsEqn(7).gif 
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    Click image for larger version. 

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    Are those steps right so far? If so, how do I solve the rest?
    There are two ways of doing this. The first is essentially what you have done sin(\pi/6)= \frac{1}{2} and cos(\pi/6)= \frac{\sqrt{3}}{2} so that z= \frac{3\sqrt{3}}{2}+ i\frac{3}{2}. \overline{z}= \frac{3\sqrt{3}}{2}- i\frac{3}{2}. All that has to be multiplied. It is simpler if you realize that (a+ bi)(a- bi)= a^2+ b^2, a real number.

    The other way is to use the exponential form. saying z= 3(cos(\pi/6)+ i sin(\pi/6)) is the same as saying z= 3e^{i\pi/6}. And then \overline{z}= 3e^{-i\pi/6}. And then the product is (3)(3)(e^{i\pi/6- i\pi/6})= 9

    2.If Click image for larger version. 

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ID:	26095 and Click image for larger version. 

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    \frac{8e^{\frac{\pi i}{2}}}{4e^{\frac{\pi i}{4}}}= \frac{8}{4}e^{\frac{\pi i}{2}- \frac{\pi i}{4}}= 2e^{\frac{\pi i}{4}}

    I got the answer 2e^(2pi/8)i

    But the correct answer is 2+i sq.rt2
    How do I get that answer?
    First if you do not know that 2/8= 1/4 you should give up all math!
    And, of course, 2e^{\pi i/4}= 2(cos(\pi/4)+ i sin(\pi/4)). What is that equal to? (It is NOT "2+ i sq.rt 2"! I suspect you have misread that.)
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