What is the distance between [(3 + 4i) + (2 – 3i)] and (9 – 2i)?

Question

What is the distance between [(3 + 4i) + (2 – 3i)] and (9 – 2i)?

in progress 0
Hải Đăng 3 months 2021-08-13T21:02:46+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-13T21:03:49+00:00

    Answer:

    5

    Step-by-step explanation:

    (3 + 4i) + (2 – 3i) = 3 + 4i + 2 – 3i = 5 + i

    distance between (5 + i) and (9 – 2i) is the difference between them. and difference means subtraction.

    (9 – 2i) – (5 + i) = 9 – 2i – 5 – i = 4 – 3i

    and since we are looking for a distance, we are looking for the absolute value of that subtraction.

    after all, we could have done the subtraction also in the other direction

    (5 + i) – (9 – 2i) = -4 + 3i

    and this must be the same distance.

    |(-4 + 3i)| = |(4 – 3i)|

    and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.

    |(a +bi)| = sqrt(a² + b²)

    in our case here

    distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5

    as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :

    sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )