How do you give the complex number form of the vector with the given initial and terminal point respectively (-2, 5) and (1, 3)?

Jun 5, 2018

$< 3 i , - 2 j >$

Explanation:

Assuming that we are given P(-2, 5) and Q(1, 3), we can use the following formula to calculate the commonly used "i and j form" of the vector:

$< \left({x}_{2} - {x}_{1}\right) i , \left({y}_{2} - {y}_{1}\right) j >$

Notice it's very similar to the slope formula, but written in point notation and using "<" instead of parentheses.

Now let's solve:

$< 1 - \left(- 2\right) , 3 - 5 >$
$< 1 + 2 , 3 - 5 >$
$< 3 i , - 2 j >$

Should you want to go on to find the magnitude of the vector, you would use the formula $\sqrt{{\left(a\right)}^{2} + {\left(b\right)}^{2}}$, with a representing i and b representing j, but those are for more intricate problems.