ADD AND SUBTRACT COMPLEX NUMBERS WORKSHEET

1. Add (-3i) and (3 + 5i).

2. Add (-6 - 2i) and (6 - 5i).

3. Add (5 + 6i) and (2 - 7i).

4. Add (5 - 6i), 5i and (7 + 6i).

5. Simplify :  (-7 + 7i) - (-7 - 3i) + (-7 - 8i).

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

7. Simplify : (1 + 6i) + (6 - 2i) - (-7 + 5i).

8. Simplify : (-5 + 7i) - (-6 + i) - (-6 + 5i).

9. Subtract (3 - 4i) from (8 + 2i).

10. Subtract (-5 - i) from (2 - 7i).

11. (4 + i) + (7 - i)

12. (-4 + 3i) - (1 - 8i)

13. (-5 + 3i) - (-2 + 6i)

14. (-3 + 8i) + (5 + 6i)

15. (-2i) - 7 - (-2 + 8i)

16. (5 - 7i) - (2 + i)

Solve the following equations for complex numbers.

17. 4 + 5i = z - (1 - i)

18. (1 + 2i)z = 2 + 5i

1. Answer :

(-3i) + (3 + 5i) = 3 + (-3i + 5i)

= 3 + 2i

2. Answer :

(-6 - 2i) + (6 - 5i) = (-6 + 6) + (-2i - 5i)

= 0 + (-7i)

= -3i

3. Answer :

(5 + 6i) + (2 - 7i) = (5 + 2) + (6i - 7i)

= 7 + (-i)

= 7 - i

4. Answer :

(5 - 6i) + 5i + (7 + 6i) = (5 + 7) + (-6i + 5i + 6i)

= 12 + 5i

5. Answer :

(-7 + 7i) - (-7 - 3i) + (-7 - 8i) = -7 + 7i  + 7 + 3i - 7 - 8i

= (-7 + 7 - 7) + (7i + 3i - 8i)

= -7 + 2i

6. Answer :

(-4 - 7i) - (4 + 5i) - (2 - i) = -4 - 7i - 4 - 5i - 2 + i

= (-4 - 4 - 2) + (-7i - 5i + i)

= -10 + (-11i)

= -10 - 11i

7. Answer :

(1 + 6i) + (6 - 2i) - (-7 + 5i) = 1 + 6i + 6 - 2i + 7 - 5i

= (1 + 6 + 7) + (6i - 2i - 5i)

= 14 + (-i)

= 14 - i

8. Answer :

(-5 + 7i) - (-6 + i) - (-6 + 5i) = -5 + 7i + 6 - i + 6 - 5i

= (-5 + 6 + 6) + (7i - i - 5i)

= 7 + i

9. Answer :

(8 + 2i) - (3 - 4i) = 8 + 2i - 3 + 4i

= (8 - 3) + (2i + 4i)

= 5 + 6i

10. Answer :

(2 - 7i) - (-5 - i) = 2 - 7i + 5 + i

= (2  + 5) + (-7i + i)

= 7 + (-6i)

= 7 - 6i

11. Answer :

= (4 + i) + (7 - i)

= 4 + i + 7 - i

= 4 + 7

= 11

12. Answer :

= (-4 + 3i) - (1 - 8i)

= -4 + 3i - 1 + 8i

= -5 + 11i

13. Answer :

 (-5 + 3i) - (-2 + 6i)

Distributing the negagtive sign, we get

= -5 + 3i + 2 - 6i

= (-5 + 2) + (3i - 6i)

= -3 - 3i

14. Answer :

= (-3 + 8i) + (5 + 6i)

= -3 + 5 + 8i + 6i

= 2 + 14i

15. Answer :

= (-2i) - 7 - (-2 + 8i)

= -2i - 7 + 2 - 8i

= -2i - 8i - 7 + 2

= -10i - 5

Writing the real part first and imaginary part next, we get

= -5 - 10i

16. Answer :

= (5 - 7i) - (2 + i)

= 5 - 7i - 2 - i

= 5 - 2 - 7i - i

= 3 - 8i

3 - 8i

Solve the following equations for complex numbers.

17. Answer :

4 + 5i = z - (1 - i)

Let z = x + iy

4 + 5i = x + iy - (1 - i)

4 + 5i = x + iy - 1 + i

4 + 5i = (x - 1) + i(y + 1)

Equating the real and imaginary parts, we get

x - 1 = 4 and y + 1 = 5

x = 4 + 1 and y = 5 - 1

x = 5 and y = 4

18. Answer :

(1 + 2i)z = 2 + 5i

Let z = x + iy

(1 + 2i)(x + iy) = 2 + 5i

x + iy + 2ix + 2i²y = 2 + 5i

x + i(y + 2x) + 2(-1)y = 2 + 5i

x - 2y + i(y + 2x) = 2 + 5i

Equating the real and imaginary parts, we get

x - 2y = 2 -----(1)

2x + y = 5 -----(2)

(1) + 2(2)

x - 2y + 4x + 2y = 2 + 10

5x = 12

x = 12/5

Applying x = 12/5 in (1),

2y = x - 2

2y = (12/5) - 2

2y = 2/5

y = 1/5

So, the values of x and y are 12/5 and 1/5 respectively.

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