Answer:
5
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