## anonymous one year ago Solve (z + 6)2 = 5. A. B. C. D.

1. anonymous

Might help: http://www.mathpapa.com/algebra-calculator.html also shows you step by step

2. anonymous

|dw:1432838616284:dw|

3. anonymous

i get confused after this?@KendrickLamar2014

4. anonymous

the answer choices didnt go through, i will wrte them out through the draw tool! @KendrickLamar2014

5. anonymous

|dw:1432838835991:dw| @KendrickLamar2014

6. anonymous

@KendrickLamar2014

7. KendrickLamar2014

My guess would be choice C, not 100% sure tho.

8. KendrickLamar2014

@Michele_Laino

9. anonymous

im in between B and c?

10. KendrickLamar2014

@Luigi0210 @kropot72

11. anonymous

help!!! @KendrickLamar2014 @ssssss @Vocaloid @AriPotta

12. Vocaloid

OH MY GOODNESS, ok, I didn't realize that the 2 was an exponent!

13. Vocaloid

that changes everything! (z + 6)^2 = 5

14. Vocaloid

take the square root of each side subtract 6 from each side

15. Luigi0210

$$\Large (z+6)^2=5$$ $$\Large \sqrt{(z+6)^2}=\sqrt{5}$$ $$\Large z+6=\pm \sqrt{5}$$ $$\Large z+6-6=\pm\sqrt{5}-6$$ $$\Large \color{green}{z=\pm\sqrt{5}-6}$$

16. KendrickLamar2014

Oh the 2 is an exponent. No wonder I could not find the answer :P

17. anonymous

oh!

18. Luigi0210

Good luck $$\Huge \color{red}{\star^{\star}}$$

19. KendrickLamar2014

20. anonymous

@Luigi0210 thats not an answer choice but whould it be c? its the closest one?

21. Vocaloid

hint: A + B = B + A

22. Michele_Laino

is z a complex number?

23. Vocaloid

when you add two terms together you can switch the order

24. anonymous

okay so my best assumption would be b or c?

25. anonymous

yes it is what it will equal up to!:) @Michele_Laino

26. Luigi0210

It's magic! $$\Large \pm \sqrt{5}-6 = \color{red}{ -6\pm \sqrt{5}}=\color{green}{-6+\sqrt{5} ~or~ -6-\sqrt{5}}$$

27. Michele_Laino

if z is a complex number, then your equation, can be rewritten as below: $\Large {\left( {x + 6 + iy} \right)^2} = 5$ wher i is such that: $\Large {i^2} = - 1$ and I have used: $\Large z = x + iy$

28. Michele_Laino

so we are led to this subsequent algebraic system: $\Large \left\{ {\begin{array}{*{20}{c}} {\left( {x + 6} \right)y = 0} \\ {{{\left( {x + 6} \right)}^2} - {y^2} = 5} \end{array}} \right.$ whose acceptable solutions are: $\Large \left\{ \begin{gathered} {x_1} = - 6 + \sqrt 5 \hfill \\ {y_1} = 0 \hfill \\ \end{gathered} \right.,\quad \left\{ {\begin{array}{*{20}{c}} {{x_2} = - 6 - \sqrt 5 } \\ {{y_2} = 0} \end{array}} \right.$