Question

which expression is equivalent to ((3 + 5i)^2)?
( -16 + 30i )
( 6 + 34i )
( -16 - 34i )
( 16 + 30i )

Explanation:

Step1: Expand using binomial rule

$(a+b)^2 = a^2 + 2ab + b^2$, so:
$$(3+5i)^2 = 3^2 + 2(3)(5i) + (5i)^2$$

Step2: Calculate each term

$$3^2=9,\ 2(3)(5i)=30i,\ (5i)^2=25i^2$$

Step3: Substitute $i^2=-1$

$$25i^2=25(-1)=-25$$

Step4: Combine all terms

$$9 + 30i -25 = (9-25)+30i=-16+30i$$

Answer:

$-16 + 30i$ (Option 1)