The expression (3 + i)(1+2i) can be written in the form a + bi, where a and b are integers. What are the values of a and b?

a = 1 and b = -7

Step-by-step explanation:

Given the expression

(3 + i)(1+2i)

On factorizing we have;

(3 + i)(1+2i)

= 3(1)+3(2i)+1(i)+i(2i)

= 3 + 6i + i + 2i²

= 3 + 7i + 2i²

Since i² = -1

The expression becomes;

= 3 + 7i + 2(-1)

= 3 + 7i -2

= 1 - 7i

On comparing with a + bi

a = 1 and b = -7

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.