# How do you give the complex number form of the vector with the given initial and terminal point respectively (4,7) and (-3, 1)?

Dec 13, 2017

The answer is $= - 7 - 6 i$

#### Explanation:

Let the point $A = \left(4 , 7\right)$ and the point $B = \left(- 3 , 1\right)$

Therefore,

${z}_{A} = 4 + 7 i$

${z}_{B} = - 3 + i$

Where, ${i}^{2} = - 1$

Then,

$\vec{A B} = {z}_{B} - {z}_{A} = \left(- 3 + i\right) - \left(4 + 7 i\right) = - 3 + 1 - 4 - 7 i$

$= - 7 - 6 i$