Equivalent expressions are expressions that have the same value
The equivalent expression of [tex](4 +7i)(3 +4i)[/tex] is [tex]-16+37i[/tex]
The expression is given as:
[tex](4 +7i)(3 +4i)[/tex]
Expand the equation
[tex](4 +7i)(3 +4i) = 4(3 +4i) +7i(3 +4i)[/tex]
Distribute the equation, as follows:
[tex](4 +7i)(3 +4i) = 12 +16i +21i +28i^2[/tex]
In complex numbers,
[tex]i^2 = -1[/tex]
So, we have:
[tex](4 +7i)(3 +4i) = 12 +16i +21i +28(-1)[/tex]
Evaluate the product
[tex](4 +7i)(3 +4i) = 12 +16i +21i -28[/tex]
Combine like terms
[tex](4 +7i)(3 +4i) = 12-28+16i +21i[/tex]
Evaluate like terms
[tex](4 +7i)(3 +4i) = -16+37i[/tex]
Hence, the equivalent expression of [tex](4 +7i)(3 +4i)[/tex] is [tex]-16+37i[/tex]
Read more about equivalent expressions at:
https://brainly.com/question/2972832
