Given:
Two complex numbers are [tex]w_1=-2+3i[/tex] and [tex]w_2=4-4i[/tex].
To find:
The complex number that can be added to [tex]w_1[/tex] to produce [tex]w_2[/tex].
Solution:
Let complex number [tex]z=[/tex] is added to [tex]w_1[/tex] to produce [tex]w_2[/tex].
[tex]w_1+z=w_2[/tex]
[tex]z=w_2-w_1[/tex]
On substituting the values, we get
[tex]z=(4-4i)-(-2+3i)[/tex]
[tex]z=4-4i+2-3i[/tex]
Combine like real and imaginary parts.
[tex]z=(4+2)+(-4-3)i[/tex]
[tex]z=6+(-7)i[/tex]
[tex]z=6-7i[/tex]
Therefore, the correct option is C.
