question\nsimplify the expression to a + bi form:\n(-11 - 5i)(-3 - 9i)
question\nsimplify the expression to a + bi form:\n(-11 - 5i)(-3 - 9i)
Answer
Explanation:
Step1: Use the FOIL method
$$ \begin{align*} (-11 - 5i)(-3 - 9i)&=(-11)\times(-3)+(-11)\times(-9i)+(-5i)\times(-3)+(-5i)\times(-9i)\ & = 33 + 99i+15i + 45i^{2} \end{align*} $$
Step2: Combine like terms and use (i^{2}=-1)
Since (i^{2}=-1), then (45i^{2}=-45). Combine the real parts ((33-45)) and the imaginary parts ((99i + 15i)): $$ \begin{align*} 33-45+(99i + 15i)&=(33 - 45)+(99 + 15)i\ &=-12+114i \end{align*} $$
Answer:
(-12 + 114i)