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chaylaceyx3

  • one year ago

if z=a+bi and -z=a-bi, solve z+6(-z)=7 for z

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  1. Michele_Laino
    • one year ago
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    hint: if z= a+ bi, then: -z = -a - bi

  2. Michele_Laino
    • one year ago
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    furthermore: z-6z=-5z

  3. chaylaceyx3
    • one year ago
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    sorry its actually the conjugate of z, not -z so its a-bi

  4. Michele_Laino
    • one year ago
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    ok! then your equation can be rewritten as follows: \[\Large z + 6\bar z = a + bi + 6a - 6bi = 7a - 5bi = 7\]

  5. Michele_Laino
    • one year ago
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    which is equivalent to these two real equations: \[\Large \left\{ \begin{gathered} 7a = 7 \hfill \\ - 5b = 0 \hfill \\ \end{gathered} \right.\] please solve that system for a and b

  6. chaylaceyx3
    • one year ago
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    a=1 and b=0 ?

  7. Michele_Laino
    • one year ago
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    that's right! so, what is z=...?

  8. chaylaceyx3
    • one year ago
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    do i just plug these numbers into 7a-5bi?

  9. Michele_Laino
    • one year ago
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    no, you have to plug, those values, for a and b, into z=a+bi

  10. Michele_Laino
    • one year ago
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    what do you get?

  11. chaylaceyx3
    • one year ago
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    so its 1?

  12. Michele_Laino
    • one year ago
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    correct! z=1 is the solution of your complex equation

  13. chaylaceyx3
    • one year ago
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    OH ok! Thanks so much!

  14. Michele_Laino
    • one year ago
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    :)

  15. chaylaceyx3
    • one year ago
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    question, where does the i go? my teacher asked and i wasn't sure

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