Question

Please help me help help me please help help me NOT A EXAM

Answer 1

So we have two complex numbers and we have to find the midpoint between them. Here is important to remember that complex numbers are composed of two parts:

`\begin{gathered} a+b\cdot i \\ a,b\text{ are real numbers} \end{gathered}`

Where a is known as the real part and b as the imaginary part with i being the imaginary unit. Complex numbers can be represented as two dimentional points with their real part as their first coordinate and their imaginary part as their second coordinate. Then the numbers we have are:

`\begin{gathered} -7+4i=(-7,4) \\ 3-2i=(3,-2) \end{gathered}`

Using this representation we can find the midpoint. The midpoint between two points (a,b) and (c,d) is given by:

`((a,b)+(c,d))/(2)=((a+c,c+d))/(2)=((a+c)/(2),(b+d)/(2))`

So the midpoint between (-7,4) and (3,-2) is given by:

`((-7,4)+(3,-2))/(2)=(-(4)/(2),(2)/(2))=(-2,1)`

Then the answer is:

`-2+1\cdot i`