Final answer:
The product of 5i and (6 - 2i) is 30i + 10, after distributing 5i and substituting i² with -1.
Step-by-step explanation:
To multiply the complex numbers 5i and (6 - 2i), we distribute 5i across the expression inside the parentheses:
5i × (6 - 2i) = 5i × 6 - 5i × 2i
This simplifies to:
30i - 10i²
Since i² equals -1, we replace i² with -1:
30i - 10(-1)
Which simplifies to:
30i + 10
Thus, the product of 5i and (6 - 2i) is 30i + 10, making the correct answer option 'b) 30i + 10'.