1. **State the problem:** We need to solve the following problems: a) $\frac{2}{3} + \frac{1}{6}$ b) $(4 + 3i) + (2 + 5i)$ c) $(7 + 4i) - (3 + i)$ d) $(2 + i)^2$ 2. **Formula and rules:** - For adding fractions: find a common denominator and add numerators. - For adding/subtracting complex numbers: add/subtract real parts and imaginary parts separately. - For squaring a complex number: use $(a + bi)^2 = a^2 + 2abi + (bi)^2 = a^2 - b^2 + 2abi$ because $i^2 = -1$. 3. **Solve each part:** a) Add fractions: $$\frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{4 + 1}{6} = \frac{5}{6}$$ b) Add complex numbers: $$(4 + 3i) + (2 + 5i) = (4 + 2) + (3i + 5i) = 6 + 8i$$ c) Subtract complex numbers: $$(7 + 4i) - (3 + i) = (7 - 3) + (4i - i) = 4 + 3i$$ d) Square the complex number: $$(2 + i)^2 = 2^2 + 2 \times 2 \times i + i^2 = 4 + 4i + (-1) = 3 + 4i$$