question\nsimplify the expression to a + bi form:\n(1 - 5i)(4 - 5i)

Explanation:

Step1: Use FOIL method

$(1 - 5i)(4 - 5i)=1\times4-1\times5i-5i\times4 + (-5i)\times(-5i)$

Step2: Calculate each term

$1\times4 = 4$, $1\times5i=5i$, $5i\times4 = 20i$, $(-5i)\times(-5i)=25i^{2}$ So the expression becomes $4-5i - 20i+25i^{2}$

Step3: Recall $i^{2}=-1$

Substitute $i^{2}=-1$ into the expression: $4-5i - 20i+25\times(-1)$

Step4: Combine like - terms

$4-25-(5i + 20i)=-21-25i$

Answer:

$-21-25i$