chaylaceyx3
  • chaylaceyx3
if z=a+bi and -z=a-bi, solve z+6(-z)=7 for z
Trigonometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Michele_Laino
  • Michele_Laino
hint: if z= a+ bi, then: -z = -a - bi
Michele_Laino
  • Michele_Laino
furthermore: z-6z=-5z
chaylaceyx3
  • chaylaceyx3
sorry its actually the conjugate of z, not -z so its a-bi

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Michele_Laino
  • Michele_Laino
ok! then your equation can be rewritten as follows: \[\Large z + 6\bar z = a + bi + 6a - 6bi = 7a - 5bi = 7\]
Michele_Laino
  • Michele_Laino
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
chaylaceyx3
  • chaylaceyx3
a=1 and b=0 ?
Michele_Laino
  • Michele_Laino
that's right! so, what is z=...?
chaylaceyx3
  • chaylaceyx3
do i just plug these numbers into 7a-5bi?
Michele_Laino
  • Michele_Laino
no, you have to plug, those values, for a and b, into z=a+bi
Michele_Laino
  • Michele_Laino
what do you get?
chaylaceyx3
  • chaylaceyx3
so its 1?
Michele_Laino
  • Michele_Laino
correct! z=1 is the solution of your complex equation
chaylaceyx3
  • chaylaceyx3
OH ok! Thanks so much!
Michele_Laino
  • Michele_Laino
:)
chaylaceyx3
  • chaylaceyx3
question, where does the i go? my teacher asked and i wasn't sure

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