Question

1. (2 + 11i)(-3 + 6i)

Explanation:

Step1: Apply distributive property (FOIL)

Multiply each term in the first complex number by each term in the second:
$(2)(-3) + (2)(6i) + (11i)(-3) + (11i)(6i)$
$= -6 + 12i - 33i + 66i^2$

Step2: Simplify using \(i^2 = -1\)

Substitute \(i^2 = -1\) into the expression:
$-6 + 12i - 33i + 66(-1)$
$= -6 + 12i - 33i - 66$

Step3: Combine like terms

Combine real parts and imaginary parts separately:
Real: $-6 - 66 = -72$
Imaginary: $12i - 33i = -21i$
Result: $-72 - 21i$

Answer:

\(-72 - 21i\)