1. ## Please check my complex numbers (Work Included)

Please check the following complex numbers and let me know if they are correct. If they are not, please point out the mistake/s I am making and what to fix You will be thanked!

Express in simplest form, in terms of i.

5. SQRT(-243)

SQRT(-243) = SQRT(81*3*(-1)) = SQRT(81)SQRT(3)SQRT(-1) = 9SQRT(3i)

6. 2[SQRT(-81)] - 2[SQRT(-100)]

2(9i) -2[SQRT(-100)]
2(9i) -2(10i)
18i - 20i
-2i

7. (2i - 5)/(i + 1)

-5 + 2i/i + 1
-5 + 2i/ 1 + i
-5 + 2i/ 1 + i * 1 - i/1 - i
(-5 + 2i)(1 - i)/2
- 3 + 7i/2

Thanks!!!!!

2. Originally Posted by bobbyboy1111
Please check the following complex numbers and let me know if they are correct. If they are not, please point out the mistake/s I am making and what to fix You will be thanked!

Express in simplest form, in terms of i.

5. SQRT(-243)

SQRT(-243) = SQRT(81*3*(-1)) = SQRT(81)SQRT(3)SQRT(-1) = 9SQRT(3i)

6. 2[SQRT(-81)] - 2[SQRT(-100)]

2(9i) -2[SQRT(-100)]
2(9i) -2(10i)
18i - 20i
-2i

7. (2i - 5)/(i + 1)

-5 + 2i/i + 1
-5 + 2i/ 1 + i
-5 + 2i/ 1 + i * 1 - i/1 - i
(-5 + 2i)(1 - i)/2
- 3 + 7i/2

Thanks!!!!!
SQRT(-243) = SQRT(81*3*(-1)) = SQRT(81)SQRT(3)SQRT(-1) = 9SQRT(3i) is incorrect, the i doesn't belong under the root

$\displaystyle \sqrt{-243}=\sqrt{81*3*-1}=\sqrt{81}\sqrt{3}\sqrt{-1}=9i\sqrt{3}$

3. Thanks! So, the rest of my problems are correct?