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Math Help - Complex Numbers

  1. #1
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    Complex Numbers

    Solve for Z when

    a) (Z+i)(1-i)=2+3i

    b) 1/z + 1/(2-i) = 3/(1+i)
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  2. #2
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    Part A

    Quote Originally Posted by djmccabie View Post
    Solve for Z when

    a) (Z+i)(1-i)=2+3i
     <br />
(Z+i)=(2+3i)/(1-i)<br />
    Z+i=[(2+3i)(1+i)] / [(1-i)(1+i)] (multiply top and bottom by 1+i)
     <br /> <br />
Z+i=(2+2i+3i+3i^2) / (1-i^2) <br />
(difference of two squares)

     <br />
Z+i=(-1+5i)/2<br />
     <br />
Z=-(1/2)+(3/2)i<br />
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  3. #3
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    Part B

    Quote Originally Posted by djmccabie View Post
    Solve for Z when

    b) 1/z + 1/(2-i) = 3/(1+i)


     <br />
(1/z)=3/(1+i)-1/(2-i)<br /> <br />
     <br />
1/z=[3(2-i)-(1+i)]/[(1+i)(2-i)]<br />
     <br />
1/z=(5-2i)/[(1+i)(2-i)]<br />
     <br />
z=(1+i)(2-i)/(5-2i)<br />
     <br />
z=(1+i)(2-i)(5+2i)/[(5-2i)(5+2i)]<br />
     <br />
z=(-1+17i)/29<br />
     <br />
z=-(1/29)+(17/29)i<br />
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