Answer
false
Work Step by Step
Square the binomial using the formula $(a+b)^2=a^2+2ab+b^2$ to obtain:
$(5+3i)^2
\\=5^2 + 2(5)(3i) + (3i)^2
\\=25 + 30i + 9i^2$
With $\sqrt{-1}=i$, the given expression simplifies to:
$=25+30i+9(\sqrt{-1})^2
\\=25+30i+9(-1)
\\=25+30i-9
\\=16+30i$
The expression above is not equal to the expression on the right side of the given equation.
Thus, the given statement is false.
