Question

which expression is equivalent to ((4 + 6i)^2)?
( -20 + 48i )
( 8 + 12i )
( 16 - 36i )
( 20 + 48i )

Explanation:

Step1: Recall the formula for squaring a binomial \((a + b)^2 = a^2 + 2ab + b^2\), here \(a = 4\), \(b = 6i\) (assuming the original problem is \((4 + 6i)^2\) as it involves imaginary numbers).

\((4 + 6i)^2 = 4^2 + 2\times4\times6i + (6i)^2\)

Step2: Calculate each term. \(4^2 = 16\), \(2\times4\times6i = 48i\), \((6i)^2 = 36i^2\). Since \(i^2 = -1\), \(36i^2 = 36\times(-1)= - 36\).

\(16 + 48i - 36\)

Step3: Combine like terms. \(16 - 36 + 48i=-20 + 48i\)

Answer:

\(-20 + 48i\) (the first option: \(-20 + 48i\))