Two complex numbers are represented by c + di and , where c, d, e, and f are positive real numbers. In what two quadrants may the product o

Question

Two complex numbers are represented by c + di and , where c, d, e, and f are positive real numbers. In what two quadrants may the product of these complex numbers lie? Explain your answer in complete sentences.

in progress 0
Ruby 3 weeks 2021-09-24T20:42:39+00:00 1 Answer 0

Answers ( )

    0
    2021-09-24T20:43:49+00:00

    Answer: In quadrant 1 or quadrant 2.

    Step-by-step explanation:

    We have the numbers:

    x = c + di

    y = e + fi

    where c, d, e and f are real positive numbers.

    the product of these numbers is:

    x*y = (c + di)*(e + fi) = c*e + c*fi + d*ei ´+d*f*i^2

    x*y = c*e – d*f + (c*f + d*e)i

    where I used that i^2 = -1

    knowing that c,f, d and e are positive numbers, then the imaginary part of the product must be always positive.

    For the real part, we have c*e – d*f, that can be positive o negative depending on the values of c, e, d, and f.

    So we have that the product must lie always in one of the upper two quadrants, quadrant 1 or quadrant 2 because the imaginary part is always positive and the real part can be positive or negative.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )