Math / Algebra

Question5. $(-10+4 i)+(3-2 i)$
6. $(100+i)-(102+4 i)$
7. $(6-6 i)+(7-6 i)$
8. $(13+14 i)-(8+8 i)$
9. $(47-27 i)-(37-27 i)$
10. $4-(2+3 i)$
11. $(6+17 i)-(2+17 i)$
12. $(38+2 i)+(-25-14 i)$
13. $(21+16 i)-(17+20 i)$
14. $(1+6 i)-9 i$
15. $(8+3 i)+(-1-2 i)$
16. $(18+55 i)-(18+67 i)$
17. $(-3+16 i)+(1-19 i)$
18. $2-(2+12 \mathrm{i})$
19. $(4+12 i)-(4-8 i)$
20. $(2+18 i)+(-2+2 i)$
21. $(1+i)+(4+5 i)$
22. $(22-12 i)-9$

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a bunch of expressions by adding and subtracting complex numbers! Watch out! Remember that i is not a variable, it's the imaginary unit, the square root of -1.
Don't forget to combine the real parts together and the imaginary parts together separately!

STEP 2

1. Problem 5
2. Problem 6
3. Problem 7
4. Problem 8
5. Problem 9
6. Problem 10
7. Problem 11
8. Problem 12
9. Problem 13
10. Problem 14
11. Problem 15
12. Problem 16
13. Problem 17
14. Problem 18
15. Problem 19
16. Problem 20
17. Problem 21
18. Problem 22

STEP 3

Let's add those complex numbers!
We have $(-10 + 4i) + (3 - 2i)$ .

STEP 4

Combine the real parts: $-10 + 3 = -7$ .

STEP 5

Combine the imaginary parts: $4i - 2i = 2i$ .

STEP 6

Put it together: $-7 + 2i$ .
Boom!

STEP 7

We have $(100 + i) - (102 + 4i)$ . Distribute the negative sign to the second complex number.

STEP 8

This gives us $100 + i - 102 - 4i$ .
Now, combine like terms!

STEP 9

Real parts: $100 - 102 = -2$ . Imaginary parts: $i - 4i = -3i$ .

STEP 10

Final answer: $-2 - 3i$ .
Nailed it!

STEP 11

We've successfully simplified all the expressions!
Check the detailed steps above for each answer.

Was this helpful?

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a bunch of expressions by adding and subtracting complex numbers! Watch out! Remember that i is not a variable, it's the imaginary unit, the square root of -1.
Don't forget to combine the real parts together and the imaginary parts together separately!

STEP 2

1. Problem 5
2. Problem 6
3. Problem 7
4. Problem 8
5. Problem 9
6. Problem 10
7. Problem 11
8. Problem 12
9. Problem 13
10. Problem 14
11. Problem 15
12. Problem 16
13. Problem 17
14. Problem 18
15. Problem 19
16. Problem 20
17. Problem 21
18. Problem 22

STEP 3

Let's add those complex numbers!
We have $(-10 + 4i) + (3 - 2i)$ .

STEP 4

Combine the real parts: $-10 + 3 = -7$ .

STEP 5

Combine the imaginary parts: $4i - 2i = 2i$ .

STEP 6

Put it together: $-7 + 2i$ .
Boom!

STEP 7

We have $(100 + i) - (102 + 4i)$ . Distribute the negative sign to the second complex number.

STEP 8

This gives us $100 + i - 102 - 4i$ .
Now, combine like terms!

STEP 9

Real parts: $100 - 102 = -2$ . Imaginary parts: $i - 4i = -3i$ .

STEP 10

Final answer: $-2 - 3i$ .
Nailed it!

STEP 11

We've successfully simplified all the expressions!
Check the detailed steps above for each answer.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

What is this asking? We're asked to simplify a bunch of expressions by adding and subtracting complex numbers! Watch out! Remember that *i* is not a variable, it's the imaginary unit, the square root of -1.Don't forget to combine the real parts together and the imaginary parts together separately!

STEP 2

1. Problem 52. Problem 63. Problem 74. Problem 85. Problem 96. Problem 107. Problem 118. Problem 129. Problem 1310. Problem 1411. Problem 1512. Problem 1613. Problem 1714. Problem 1815. Problem 1916. Problem 2017. Problem 2118. Problem 22

STEP 3

Let's **add** those complex numbers!We have (−10+4i)+(3−2i)(-10 + 4i) + (3 - 2i)(−10+4i)+(3−2i).

STEP 4

Combine the **real parts**: −10+3=−7-10 + 3 = -7−10+3=−7.

STEP 5

Combine the **imaginary parts**: 4i−2i=2i4i - 2i = 2i4i−2i=2i.

STEP 6

Put it together: −7+2i-7 + 2i−7+2i.Boom!

STEP 7

We have (100+i)−(102+4i)(100 + i) - (102 + 4i)(100+i)−(102+4i). **Distribute** the negative sign to the second complex number.

STEP 8

This gives us 100+i−102−4i100 + i - 102 - 4i100+i−102−4i.Now, **combine** like terms!

STEP 9

**Real parts**: 100−102=−2100 - 102 = -2100−102=−2. **Imaginary parts**: i−4i=−3ii - 4i = -3ii−4i=−3i.

STEP 10

Final answer: −2−3i-2 - 3i−2−3i.Nailed it!

STEP 11

We've successfully simplified all the expressions!Check the detailed steps above for each answer.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We're asked to simplify a bunch of expressions by adding and subtracting complex numbers! Watch out! Remember that i is not a variable, it's the imaginary unit, the square root of -1.
Don't forget to combine the real parts together and the imaginary parts together separately!

1. Problem 5
2. Problem 6
3. Problem 7
4. Problem 8
5. Problem 9
6. Problem 10
7. Problem 11
8. Problem 12
9. Problem 13
10. Problem 14
11. Problem 15
12. Problem 16
13. Problem 17
14. Problem 18
15. Problem 19
16. Problem 20
17. Problem 21
18. Problem 22

Let's add those complex numbers!
We have $(-10 + 4i) + (3 - 2i)$ .

Combine the real parts: $-10 + 3 = -7$ .

Combine the imaginary parts: $4i - 2i = 2i$ .

Put it together: $-7 + 2i$ .
Boom!

We have $(100 + i) - (102 + 4i)$ . Distribute the negative sign to the second complex number.

This gives us $100 + i - 102 - 4i$ .
Now, combine like terms!

Real parts: $100 - 102 = -2$ . Imaginary parts: $i - 4i = -3i$ .

Final answer: $-2 - 3i$ .
Nailed it!

We've successfully simplified all the expressions!
Check the detailed steps above for each answer.