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

You must have the hang of it. I thought these should be:

1: sqrt( 8^2 + 6^2)=sqrt(64+36)=sqrt(100)=10
10:|sqrt(8)-i*sqrt(4)| = sqrt( (sqrt(8))^2 + (sqrt(4))^2)
= sqrt(8+4) = sqrt(12)=2*sqrt(3)

Answer 2

You got almost all the addition ones right, although I saw one careless error (on #7), so you should check your work.

You only got about half the ones right where you're supposed to take the norm. To get the norm, you always square the real part, square the coefficient of i, add the results together, and take the square root. So it's just like distance in the xy-plane.

For example, on #1, take 8^2 + 6^2 = 100, and take the square root, namely 10. That's your answer. On #8 you had the right idea but evidently made a slight error in addition. On #10, it's just the square root of 8+4 (of course, you should simplify that). Similarly, #9 is the square root of 4+36 (again, you should simplify).