Question

a) plot each complex number.

1. 6 - 6i
2. -12 + 15i
3. -9 - 6i
4. 6
5. 15 - 12i
6. -9i

b) what complex number does each point represent?
7)
8)
9)

Explanation:

Part A: Plotting Complex Numbers

A complex number \( a + bi \) is plotted on the complex plane where the real part (\( a \)) corresponds to the \( x \)-axis (Real, \( R \)) and the imaginary part (\( b \)) corresponds to the \( y \)-axis (Imaginary, \( Im \)).

1. \( 6 - 6i \)

• Real part: \( 6 \) (move 6 units right on \( R \)-axis).
• Imaginary part: \( -6 \) (move 6 units down on \( Im \)-axis).
• Plot the point \( (6, -6) \).

2. \( -12 + 15i \)

• Real part: \( -12 \) (move 12 units left on \( R \)-axis).
• Imaginary part: \( 15 \) (move 15 units up on \( Im \)-axis).
• Plot the point \( (-12, 15) \).

3. \( -9 - 6i \)

• Real part: \( -9 \) (move 9 units left on \( R \)-axis).
• Imaginary part: \( -6 \) (move 6 units down on \( Im \)-axis).
• Plot the point \( (-9, -6) \).

4. \( 6 \) (or \( 6 + 0i \))

• Real part: \( 6 \) (move 6 units right on \( R \)-axis).
• Imaginary part: \( 0 \) (stay on the \( R \)-axis).
• Plot the point \( (6, 0) \).

5. \( 15 - 12i \)

• Real part: \( 15 \) (move 15 units right on \( R \)-axis).
• Imaginary part: \( -12 \) (move 12 units down on \( Im \)-axis).
• Plot the point \( (15, -12) \).

6. \( -9i \) (or \( 0 - 9i \))

• Real part: \( 0 \) (stay on the origin’s \( R \)-axis).
• Imaginary part: \( -9 \) (move 9 units down on \( Im \)-axis).
• Plot the point \( (0, -9) \).

Part B: Identifying Complex Numbers from Points

For a point \( (x, y) \) on the complex plane, the complex number is \( x + yi \) (where \( x \) = real part, \( y \) = imaginary part).

7. Points:

• Point A: \( (-15, 0) \) → \( -15 + 0i = -15 \).
• Point B: \( (0, 25) \) → \( 0 + 25i = 25i \).
• Point C: \( (15, 15) \) → \( 15 + 15i \).

8. Points:

• Point D: \( (-6, 3) \) → \( -6 + 3i \).
• Point E: \( (0, -9) \) → \( 0 - 9i = -9i \).
• Point F: \( (8, 0) \) → \( 8 + 0i = 8 \).

9. Points:

• Point I: \( (0, 16) \) → \( 0 + 16i = 16i \).
• Point H: \( (0, -8) \) → \( 0 - 8i = -8i \).
• Point G: \( (-16, -16) \) → \( -16 - 16i \).

Final Answers (Key Examples):

• A1: Plot \( (6, -6) \) for \( 6 - 6i \).
• B7 (Point A): \( \boldsymbol{-15} \).
• B8 (Point F): \( \boldsymbol{8} \).
• B9 (Point I): \( \boldsymbol{16i} \).

(Note: For plotting, mark the coordinates on the provided grids as described. For part B, use the \( (x, y) \) to \( x + yi \) conversion.)

Answer:

Part A: Plotting Complex Numbers

A complex number \( a + bi \) is plotted on the complex plane where the real part (\( a \)) corresponds to the \( x \)-axis (Real, \( R \)) and the imaginary part (\( b \)) corresponds to the \( y \)-axis (Imaginary, \( Im \)).

1. \( 6 - 6i \)

• Real part: \( 6 \) (move 6 units right on \( R \)-axis).
• Imaginary part: \( -6 \) (move 6 units down on \( Im \)-axis).
• Plot the point \( (6, -6) \).

2. \( -12 + 15i \)

• Real part: \( -12 \) (move 12 units left on \( R \)-axis).
• Imaginary part: \( 15 \) (move 15 units up on \( Im \)-axis).
• Plot the point \( (-12, 15) \).

3. \( -9 - 6i \)

• Real part: \( -9 \) (move 9 units left on \( R \)-axis).
• Imaginary part: \( -6 \) (move 6 units down on \( Im \)-axis).
• Plot the point \( (-9, -6) \).

4. \( 6 \) (or \( 6 + 0i \))

• Real part: \( 6 \) (move 6 units right on \( R \)-axis).
• Imaginary part: \( 0 \) (stay on the \( R \)-axis).
• Plot the point \( (6, 0) \).

5. \( 15 - 12i \)

• Real part: \( 15 \) (move 15 units right on \( R \)-axis).
• Imaginary part: \( -12 \) (move 12 units down on \( Im \)-axis).
• Plot the point \( (15, -12) \).

6. \( -9i \) (or \( 0 - 9i \))

• Real part: \( 0 \) (stay on the origin’s \( R \)-axis).
• Imaginary part: \( -9 \) (move 9 units down on \( Im \)-axis).
• Plot the point \( (0, -9) \).

Part B: Identifying Complex Numbers from Points

For a point \( (x, y) \) on the complex plane, the complex number is \( x + yi \) (where \( x \) = real part, \( y \) = imaginary part).

7. Points:

• Point A: \( (-15, 0) \) → \( -15 + 0i = -15 \).
• Point B: \( (0, 25) \) → \( 0 + 25i = 25i \).
• Point C: \( (15, 15) \) → \( 15 + 15i \).

8. Points:

• Point D: \( (-6, 3) \) → \( -6 + 3i \).
• Point E: \( (0, -9) \) → \( 0 - 9i = -9i \).
• Point F: \( (8, 0) \) → \( 8 + 0i = 8 \).

9. Points:

• Point I: \( (0, 16) \) → \( 0 + 16i = 16i \).
• Point H: \( (0, -8) \) → \( 0 - 8i = -8i \).
• Point G: \( (-16, -16) \) → \( -16 - 16i \).

Final Answers (Key Examples):

• A1: Plot \( (6, -6) \) for \( 6 - 6i \).
• B7 (Point A): \( \boldsymbol{-15} \).
• B8 (Point F): \( \boldsymbol{8} \).
• B9 (Point I): \( \boldsymbol{16i} \).

(Note: For plotting, mark the coordinates on the provided grids as described. For part B, use the \( (x, y) \) to \( x + yi \) conversion.)