Worksheet for graphing and writing complex numbers, including six exercises with coordinate grids.

Let’s solve each problem step by step.

We’re working with complex numbers on a coordinate plane.
The horizontal axis is the Real part (like x-axis).
The vertical axis is the Imaginary part (like y-axis).

A complex number like a + bi means:
→ Go a units right (or left if negative) on the Real axis.
→ Then go b units up (or down if negative) on the Imaginary axis.
→ Put a dot there — that’s your point!

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Problem 1: Graph 5 + 5i

- Real part = 5 → move 5 to the right.
- Imaginary part = 5 → move 5 up.
- Plot point at (5, 5)

✔ Done for #1.

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Problem 2: Graph -4 - 3i

- Real part = -4 → move 4 to the left.
- Imaginary part = -3 → move 3 down.
- Plot point at (-4, -3)

✔ Done for #2.

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Problem 3: Graph 2 - 5i

- Real part = 2 → move 2 to the right.
- Imaginary part = -5 → move 5 down.
- Plot point at (2, -5)

✔ Done for #3.

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Now problems 4–6 are reversed: we see a graphed point and must write the complex number.

Look at where the red dot is:

Problem 4: Point is at (-4, -5)

- Real part = -4 (x-coordinate)
- Imaginary part = -5 (y-coordinate)
→ So complex number is: -4 - 5i

✔ Done for #4.

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Problem 5: Point is at (-2, -3)

Wait — let me check the image again carefully.

In problem 5, the red dot is at:
→ Real axis: -2 (two left)
→ Imaginary axis: -3 (three down)

So complex number = -2 - 3i

✔ Done for #5.

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Problem 6: Point is at (3, -5)

Red dot is at:
→ Real axis: 3 (three right)
→ Imaginary axis: -5 (five down)

So complex number = 3 - 5i

✔ Done for #6.

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Let me double-check all answers:

1) 5 + 5i → (5,5) ✔️
2) -4 - 3i → (-4,-3) ✔️
3) 2 - 5i → (2,-5) ✔️
4) Graph shows (-4,-5) → -4 - 5i ✔️
5) Graph shows (-2,-3) → -2 - 3i ✔️
6) Graph shows (3,-5) → 3 - 5i ✔️

All correct.

Final Answer:
1) Graph point at (5, 5)
2) Graph point at (-4, -3)
3) Graph point at (2, -5)
4) -4 - 5i
5) -2 - 3i
6) 3 - 5i