Adding and Subtracting Complex Numbers online exercise for | Live ... - Free Printable

Let’s solve each problem step by step. We’re adding and subtracting complex numbers — that means we combine the real parts (numbers without “i”) and the imaginary parts (numbers with “i”) separately.

Remember:
- Real + Real = Real
- Imaginary + Imaginary = Imaginary
- i is like a variable — you can’t add it to a regular number, only to other “i” terms.

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1) (-i) + (6i)
→ -1i + 6i = 5i

2) (-6i) - (6i)
→ -6i - 6i = -12i

3) (-4i) - (5i)
→ -4i - 5i = -9i

4) (-3i) + (3 + 5i)
→ Group real and imaginary:
Real: 0 + 3 = 3
Imaginary: -3i + 5i = 2i
→ 3 + 2i

5) (-2i) + (5i)
→ -2i + 5i = 3i

6) (3i) + (4i)
→ 3i + 4i = 7i

7) (-6 - 2i) + (6 - 5i)
→ Real: -6 + 6 = 0
→ Imaginary: -2i - 5i = -7i
→ 0 - 7i or just -7i

8) (-5 + 3i) - (4 - 5i)
→ Distribute the minus sign: -5 + 3i - 4 + 5i
→ Real: -5 - 4 = -9
→ Imaginary: 3i + 5i = 8i
→ -9 + 8i

9) (5 + 6i) + (2 - 7i)
→ Real: 5 + 2 = 7
→ Imaginary: 6i - 7i = -1i
→ 7 - i

10) (6 - 8i) - (4i) + 7
→ First, rewrite: 6 - 8i - 4i + 7
→ Real: 6 + 7 = 13
→ Imaginary: -8i - 4i = -12i
→ 13 - 12i

11) (3 - 4i) - (-5 + 7i)
→ Distribute minus: 3 - 4i + 5 - 7i
→ Real: 3 + 5 = 8
→ Imaginary: -4i - 7i = -11i
→ 8 - 11i

12) (5 + 3i) - (-2 - 5i)
→ Distribute minus: 5 + 3i + 2 + 5i
→ Real: 5 + 2 = 7
→ Imaginary: 3i + 5i = 8i
→ 7 + 8i

13) (5 - 6i) + (5i) + (7 + 6i)
→ Combine all:
Real: 5 + 0 + 7 = 12
Imaginary: -6i + 5i + 6i = 5i
→ 12 + 5i

14) (-7 + 7i) - (-7 - 3i) + (-7 - 8i)
→ Distribute minuses:
= -7 + 7i + 7 + 3i - 7 - 8i
→ Real: -7 + 7 - 7 = -7
→ Imaginary: 7i + 3i - 8i = 2i
→ -7 + 2i

15) (-4 - 7i) - (4 + 5i) - (2 - i)
→ Distribute minuses:
= -4 - 7i - 4 - 5i - 2 + i
→ Real: -4 - 4 - 2 = -10
→ Imaginary: -7i - 5i + i = -11i
→ -10 - 11i

16) (-1 + i) - (-7 + 4i) - 5
→ Distribute minus:
= -1 + i + 7 - 4i - 5
→ Real: -1 + 7 - 5 = 1
→ Imaginary: i - 4i = -3i
→ 1 - 3i

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Final Answer:
1) 5i
2) -12i
3) -9i
4) 3 + 2i
5) 3i
6) 7i
7) -7i
8) -9 + 8i
9) 7 - i
10) 13 - 12i
11) 8 - 11i
12) 7 + 8i
13) 12 + 5i
14) -7 + 2i
15) -10 - 11i
16) 1 - 3i