Answer:
[tex](x+3i)^2-(2x-3i)^2=-3x^2+18xi[/tex]
Step-by-step explanation:
we are given
[tex](x+3i)^2-(2x-3i)^2[/tex]
we can use formula
[tex](a+b)^2=a^2+2ab+b^2[/tex]
[tex](x+3i)^2=x^2+2\times x\times 3i+(3i)^2[/tex]
[tex](x+3i)^2=x^2+6xi-9[/tex]
[tex](2x-3i)^2=(2x)^2-2\times 2x\times 3i+(3i)^2[/tex]
[tex](2x-3i)^2=4x^2-12xi-9[/tex]
now, we can plug values
[tex](x+3i)^2-(2x-3i)^2=(x^2+6xi-9)-(4x^2-12xi-9)[/tex]
now, we can simplify it
we get
[tex](x+3i)^2-(2x-3i)^2=-3x^2+18xi[/tex]
