If Z1 = 12 + 6݅ and Z2 = a + bi (where a, b ∈ R) are two complex number, we can say that the product Z1Z2is imaginary A) If and only if ܽ = ܾ = 0 B) If b = 2a C) If a = −2b D) for each value of a and b

A) if and only if a = 0

Step-by-step explanation:

Since Z1 = 12 + 6݅  and Z2 = a + bi , then the product, Z1Z2 = (12 + 6)(a + bi)

Z1Z2 = (12 + 6)(a + bi)

Expanding the brackets, we have

Z1Z2 = 12a + 12bi + 6a + 6bi

Collecting like terms, we have

Z1Z2 = 12a + 6a + 12bi +6bi

Z1Z2 = 12a + 6a + (12b +6b)i

Simplifying, we have

Z1Z2 = 18a + 18bi

For Z1Z2 to be imaginary, then the real part must be zero.

That is 18a = 0 ⇒ a = 0

So, Z1Z2 is imaginary if and only if a = 0

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,