Questions: Multiply. (4-3 j)^2 (4-3 j)^2= (Simplify your answer. Type your answer in the form a + bj.)

Solution Steps

To solve \((4 - 3j)^2\), we can use the formula for the square of a binomial: \((a - b)^2 = a^2 - 2ab + b^2\). Here, \(a = 4\) and \(b = 3j\). We will apply this formula to find the real and imaginary parts of the result.

We start with the expression \((4 - 3j)^2\). Using the binomial expansion formula, we have: \[ (4 - 3j)^2 = 4^2 - 2 \cdot 4 \cdot (3j) + (3j)^2 \]

Calculating each term:

• \(4^2 = 16\)
• \(-2 \cdot 4 \cdot (3j) = -24j\)
• \((3j)^2 = 9j^2 = 9(-1) = -9\)

Now, we combine the results: \[ (4 - 3j)^2 = 16 - 24j - 9 = 7 - 24j \]

Final Answer