## 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)?

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1 month 2021-08-13T21:02:46+00:00 1 Answers 0 views 0

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