https://r2.erweima.ai/mathbot/image/1726493927188awmhg3lj.jpg

Let's solve the three addition problems displayed in the image step by step.

### g. \( \left( \frac{2}{5}i + \frac{2}{3} \right) + \left( -\frac{2}{3} + i \right) \)

1. Combine real parts: \( \frac{2}{3} + \left( -\frac{2}{3} \right) = 0 \)
2. Combine imaginary parts: \( \frac{2}{5}i + i = \frac{2}{5}i + \frac{5}{5}i = \frac{7}{5}i \)

Result: 
\[
g = \frac{7}{5}i
\]

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### h. \( (5 - 2i) + (3 - 2i) \)

1. Combine real parts: \( 5 + 3 = 8 \)
2. Combine imaginary parts: \( -2i + (-2i) = -4i \)

Result: 
\[
h = 8 - 4i
\]

---

### i. \( (5 - 2i) + (2 - 3i) + (2 - i) \)

1. Combine real parts: \( 5 + 2 + 2 = 9 \)
2. Combine imaginary parts: \( -2i + (-3i) + (-i) = -6i \)

Result: 
\[
i = 9 - 6i
\]

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Would you like further details or explanations on any of these? Here are some related questions for practice:

1. What is the sum of \( (3 + 4i) + (2 - i) \)?
2. How do you multiply complex numbers, such as \( (1 + i) \times (2 - i) \)?
3. What is the conjugate of \( 5 + 7i \)?
4. Solve \( (1 - 3i) + (-4 + 6i) \).
5. Subtract \( (6 - 2i) - (3 + 4i) \).

**Tip**: When adding or subtracting complex numbers, treat the real and imaginary parts separately.

This page covers the addition of complex numbers with detailed step-by-step solutions for problems like (5 - 2i) + (3 - 2i) and (5 - 2i) + (2 - 3i) + (2 - i). Ideal for students in Grades 9-11 learning complex number operations.

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