Answer
$\frac{1}{4}-\frac{9}{8}i=0.25 - 1.125 i$
Work Step by Step
Step 1: Multiplication of complex numbers works like multiplication of polynomials.
Use distributive property
$(0.5-i)\left(1-\frac{i}{4}\right)=0.5\left(1-\frac{i}{4}\right)-i\left(1-\frac{i}{4}\right)$
Step 2: Again, use distributive property
$(0.5-i)\left(1-\frac{i}{4}\right)=0.5(1)-0.5\left(\frac{i}{4}\right)-i(1)-i\left(-\frac{i}{4}\right)$
Step 3: Use $0.5=\frac{1}{2}$ and simplify
$(0.5-i)\left(1-\frac{i}{4}\right)=\frac{1}{2}-\frac{i}{8}-i+\frac{i^2}{4}$
Step 4: Use $i^2=-1$
$(0.5-i)\left(1-\frac{i}{4}\right)=\frac{1}{2}-\frac{i}{8}-i+\frac{-1}{4}$
Step 5: Add real terms with real and imaginary with imaginary,
$(0.5-i)\left(1-\frac{i}{4}\right)=\frac{1}{2}-\frac{1}{4}-\frac{i}{8}-\frac{i}{1}$
Step 6: Simplify
$(0.5-i)\left(1-\frac{i}{4}\right)=\frac{2-1}{4}+\frac{-i-8i}{8}=\frac{1}{4}+\frac{-9i}{8}=\frac{1}{4}-\frac{9}{8}i$
Step 7: $\frac{1}{4}-\frac{9}{8}i=0.25 - 1.125 i$
Step 8: The Cartesian form of $(0.5-i)\left(1-\frac{i}{4}\right)$ is $0.25 - 1.125 i$
