multiply the complex numbers (4 - 6i) and (8 - 5i).\na 2 + 68i\nb 2 - 68i\nc 62 - 28i\nd 62 + 28i

Explanation:

Step1: Use the FOIL method

$$(4 - 6i)(8 - 5i)=4\times8+4\times(- 5i)-6i\times8+(-6i)\times(-5i)$$

Step2: Calculate each term

• Calculate (4\times8 = 32)
• Calculate (4\times(-5i)=-20i)
• Calculate (-6i\times8=-48i)
• Calculate ((-6i)\times(-5i)=30i^{2})

Since (i^{2}=-1), then (30i^{2}=-30)

Step3: Combine like - terms

[ \begin{align*} &32-20i - 48i-30\ =&(32 - 30)+(-20i-48i)\ =&2-68i \end{align*} ]

Answer:

B. (2 - 68i)