Answer: x² + 2xy + y² = 9
x² + 2xy + y² = (x + y)²
with x = 2 + 3i and y = [tex]\frac{3+i}{i}[/tex], we have:
[tex](x + y)^{2}=(2+3i+\frac{3+i}{i})^{2}\\\\=(\frac{2i+3i^{2}+3+i }{i})^{2}\\\\=(\frac{3i-3+3}{i})^{2} \\\\=(\frac{3i}{i})^{2}\\\\=3^{2}=9[/tex]
Step-by-step explanation:
