Here are the solutions to your questions: 1. Given $z = \frac{2-i}{1+i}$. a) Express $z$ in the form $a+bi$. Step 1: Multiply the numerator and denominator by the conjugate of the denominator. $$ z = \frac{2-i}{1+i} \times \frac{1-i}{1-i} $$ Step 2: Perform the multiplication. Numerator: $(2-i)(1-i) = 2(1) + 2(-i) - i(1) - i(-i) = 2 - 2i - i + i^2 = 2 - 3i - 1 = 1 - 3i$. Denominator: $(1+i)(1-i) = 1^2 - i^2 = 1 - (-1) = 1+1 = 2$. Step 3: Write $z$ in the form $a+bi$. $$ z = \frac{1-3i}{2} = \frac{1}{2} - \frac{3}{2}i $$ The final answer is $\boxed{z = \frac{1}{2} - \frac{3}{2}i}$. *b) Calculate $|