Question

5. Question 3 asked for two possible quadrant locations of the product of c + di and , where c, d, e, and f are positive real numbers. The product in question 4 was two complex numbers of the form c + di and , where c, d, e, and f are positive real numbers. You answered the quadrant location of this product.

Provide an example of two complex numbers in the form c + di and , where c, d, e, and f are positive real numbers such that their product lies in the other possible quadrant. Support your example by determining its product.

Answer 1

1 + i and 2 + 3i

Explanation:

Formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

……………………………………………………………

if c, d, e, and f are positive real numbers

then

c f + d e is a positive number.

then

The product of the two complex numbers

lies in Quadrant 1 or Quadrant 2.

Since , c, d, e, and f are positive real numbers

Then

The two complex numbers c + d i and e + f i lie in Quadrant 1

We want to find an example of two complex numbers

That lie in Quadrant 1 ,such that ,their product lies in the other possible

Quadrant, which is Quadrant 2.

EXAMPLE:

Let c + d i = 1 + i

e + f i = 2 + 3i

By applying the formula:

(c + d i)(e + f i) = (c e - d f) + (c f + d e) i

We get :

(1 + i)(2 + 3i) = -1 + 5i