iop360 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. iop360

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

2. math>philosophy

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. iop360

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

4. iop360

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

5. iop360

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

6. iop360

it means to flip the sign of the imaginary part

7. math>philosophy

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

8. iop360

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

9. math>philosophy

Can you draw the question instead?

10. iop360

|dw:1353720314063:dw|

11. tkhunny

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

12. iop360

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

13. math>philosophy

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

14. math>philosophy

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. iop360

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

17. iop360

is z considered real or imaginary?

18. iop360

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. math>philosophy

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. iop360

no

23. iop360

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

24. iop360

you equate this to 9+i?

25. tkhunny

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

26. iop360

thanks