Answer:
[tex](x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16[/tex]
Step-by-step explanation:
Complex numbers identity:
The complex numbers identity is:
[tex]i^2 = -1[/tex]
Square of the sum:
[tex](x + y)^2 = x^2 + 2xy + y^2[/tex]
In this question:
[tex](x + (3+5i))^2[/tex]
[tex]x^2 + 2x(3+5i) + (3+5i)^2[/tex]
[tex]x^2 + 6x + 10xi + 9 + 30i + 25i^2[/tex]
[tex]x^2 + 6x + 9 + (10x+30)i - 25[/tex]
[tex]x^2 + 6x + (10x+30)i - 16[/tex]
So
[tex](x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16[/tex]