## anonymous one year ago One solution to a quadratic equation is x equals start fraction negative nine plus 21 i over three end fraction full stop What is the solution in simplified standard form, x = a + bi, if a and b are real numbers? Help please

1. Mertsj

$\frac{-9+21i}{3}=\frac{-9}{3}+\frac{21i}{3}=-3+7i$

2. anonymous

Thank you bunches. :) Can you help me with 2 more?

3. Mertsj

Possibly

4. anonymous

The complex solution to a quadratic equation is x equals start fraction negative four plus or minus square root of negative 80 end square root over four end fraction full stop Write this solution in standard form, x = a ± bi, where a and b are real numbers.

5. anonymous

$x=\frac{-4\pm\sqrt{-80}}{4}$?

6. anonymous

yes

7. anonymous

ok we look for the largest perfect square that is a factor of 80 i get 16 because $$80=16\times 5$$

8. anonymous

okay that makes sense

9. anonymous

therefore $\sqrt{-80}=\sqrt{16\times 5\times (-1)}=4\sqrt{5}i$

10. anonymous

woah you lost me D: lol

11. anonymous

i guess i skipped a step $\sqrt{16\times 5\times (-1)}=\sqrt{16}\sqrt{5}\sqrt{-1}=4\sqrt{5}i$

12. anonymous

since $$\sqrt{16}=4$$ and $$\sqrt{-1}$$ gets written as $$i$$

13. anonymous

that is why we were looking for the largest perfect square that is a factor of 80

14. anonymous

let me know when we can continue, it is not over yet

15. anonymous

okay that makes sense

16. anonymous

that was the hard part though now we have $\frac{-4\pm4\sqrt{5}i}{4}$divide each part of the numerator by $$4$$ and you are done

17. anonymous

this is what you have to do for all of them write the radical in simplest radical form for example since $$25\times2=50$$ you would have $\sqrt{-50}=5\sqrt{2}i$

18. anonymous

The number root of order five of ninety one to the power of four end power can be written as ninety one to the power of start fraction cap a over cap b end fraction end power. What is the value of A?