## 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

hint: if z= a+ bi, then: -z = -a - bi

2. Michele_Laino

furthermore: z-6z=-5z

3. chaylaceyx3

sorry its actually the conjugate of z, not -z so its a-bi

4. Michele_Laino

ok! then your equation can be rewritten as follows: $\Large z + 6\bar z = a + bi + 6a - 6bi = 7a - 5bi = 7$

5. 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

6. chaylaceyx3

a=1 and b=0 ?

7. Michele_Laino

that's right! so, what is z=...?

8. chaylaceyx3

do i just plug these numbers into 7a-5bi?

9. Michele_Laino

no, you have to plug, those values, for a and b, into z=a+bi

10. Michele_Laino

what do you get?

11. chaylaceyx3

so its 1?

12. Michele_Laino

correct! z=1 is the solution of your complex equation

13. chaylaceyx3

OH ok! Thanks so much!

14. Michele_Laino

:)

15. chaylaceyx3

question, where does the i go? my teacher asked and i wasn't sure