Can you check if my complex numbers (they're not hard just complex...) math answers are correct?

Question

If I get one wrong can you tell me the right answer and maybe the steps you took to get there, thank you.

GIVE EACH ABSOLUTE VALUE

i= imaginary number
I...I absolute value brackets

1.
I 8 - 6i I
A: square root of 28

2.
I -1 I
A: 1

3. I -12 + 22.5i I
A: square root of 362.25

4.
I 19i I
A: 19

ADD EACH PAIR OF COMPLEX NUMBERS

5. ( 2 + i ) + (-3 + 2i)
A: -1 + 3i

6.
( -5 + 4i ) + 3
A: -2 + 4i

7.
( 6 - 3i ) + ( -4 - 2i )
A: 2 + 5i

GIVE EACH ABSOLUTE VALUE

8.
I 15 + 7i I
A: square root of 274

9.
I -2 - 6i I
A: 2i times the square root of 10

10.
I square root of 8 - i times the square root of 4 I
A: Can you show me the steps on how you got this one, thx

11.
I 0.2 + 0.8i I
A: square root of .68

12.
I -14 I
A: 14

13.
I -3.6i I
A: 3.6

14.
I 20 + 21i I
A: 29

15. I -30 - 5.5i I
A: 30.5

ADD EACH PAIR OF COMPLEX NUMBERS

16.
( 3i ) + ( 8 )
A: 3i + 8

17.
( -4 - 3i ) + ( 2 - 2i )
A: -2 - 5i

18.
( 3 + 3i ) + ( 3 - 3i)
A: 6

19.
( 2 + 3i ) + ( 3 + 2i )
A: 5 + 5i

Answer 1

first of all this is way too many problems to post here, we are eager to help, but not to do an entire hw set; post a few representative questions from which you can get the idea of how to finish your work

1) Abs[8-6i]=sqrt[8^2+6^2]=10
3)Abs[-12+22.5i]=
sqrt[(-12)^2+22.5^2]=25.5

Answer 2

1.
I 8 - 6i I
A: square root of 28
I 8 - 6i I = √(8^2 + (-6)^2) = √(64 + 36) = √100 = 10
(Complex numbers are treated as vectors with the "real" value orthoganol to the "imaginary" value.)

3. I -12 + 22.5i I
A: square root of 362.25
√(144 + 506.25) = √650.25 = 25.5

7.
( 6 - 3i ) + ( -4 - 2i )
A: 2 + 5i
( 6 - 3i ) + ( -4 - 2i ) = 6 - 4 - 3i - 2i = 2 - 5i

8. correct

9.
I -2 - 6i I
A: 2i times the square root of 10
I -2 - 6i I = √(4 + 36) = √40 = 2√10

10.
I square root of 8 - i times the square root of 4 I
A: Can you show me the steps on how you got this one, thx
|8 - i| = √65
(√65)(√4) = 2√65

11. correct

12. correct

13. correct

14.
I 20 + 21i I = √841

15. correct

16-19 are correct

Answer 3

| a + ib| = | a - ib| = root (a^2+b^2)