## anonymous 3 years ago solve for z, and give your answer in the form a + bi (conj)z+2z = 2+4i+conj(7+3i) **conj refers to conjugate of a complex number (a line on top of it)

1. anonymous

answer is 3+i (need to learn how to do it)

2. anonymous

I don't understand the notation of the equation. Why did you put (conj)? Does it mean take the conjugate of the term that follows it? Or multiply that term by its conjugate? Or what?

3. anonymous

i dont know how to write a line above the letter for this

4. anonymous

so for this question, there would be a line above the z and the 7+3i

5. anonymous

z = a + bi (conj)z = a - bi

6. anonymous

it means to flip the sign of the imaginary part

7. anonymous

So why don't you just write z - 2z = 2 + 4i + (7 - 3i)? Is that what the question says?

8. anonymous

no, there is no line above the z+2z, just the z

9. anonymous

Can you draw the question instead?

10. anonymous

|dw:1353720314063:dw|

11. tkhunny

$$\bar{z} + 2z = 2 + 4i + \overline{7+3i} = 2 + 4i + 7 - 3i = 9 + i$$

12. anonymous

answer is 3+i though...you seem to be on the right track though

13. anonymous

no idea what the conjugate of a variable means...

14. anonymous

unless you use fourier which i don't think you are

15. tkhunny

It's not my problem statement. You need to be on the right track. Where shall we go from here? $$\bar{z} + 2z = 9 + i$$

16. anonymous

i dont know what the z part is. that is the problem

17. anonymous

is z considered real or imaginary?

18. anonymous

i tried it with both for hours

19. tkhunny

Please read the problem statement. "solve for z, and give your answer in the form a + bi" z is a Complex Number

20. anonymous

oh

21. tkhunny

You tried what? $$\bar{z} + 2z = a - bi + 2(a + bi) = a - bi + 2a + 2bi = (a + 2a) + (2b-b)i$$ Do yuo see where this is going?

22. anonymous

no

23. anonymous

i understand why you get this but why did you do this

24. anonymous

you equate this to 9+i?

25. tkhunny

That is it! $$3a + bi = 9 + i$$

26. anonymous

thanks