Question

which of the following is equivalent to the expression (3 + 2i)·(4i)·(2 + 5i)? (1 point)
(3 + 2i)+(4i)+(2 + 5i)
(3 + 2i)·4i + 2 + 5i
(3 + 2i)·(4i)·(2 + 5i)
12i + 8·(2 + 5i)

Explanation:

Step1: Recall associative property of complex - number multiplication

For complex numbers \(a\), \(b\), and \(c\), \((a\cdot b)\cdot c=a\cdot(b\cdot c)\). Here \(a = 3 + 2i\), \(b = 4i\), and \(c=2 + 5i\).

Step2: Apply the associative property

The expression \([(3 + 2i)\cdot(4i)]\cdot(2 + 5i)\) is equivalent to \((3 + 2i)\cdot[(4i)\cdot(2 + 5i)]\) by the associative property of multiplication of complex numbers.

Answer:

\((3 + 2i)\cdot[(4i)\cdot(2 + 5i)]\)