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expressions that are equivalent to the complex expression left-parenthesis 3 x plus 5 i right-parenthesis squared

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To simplify the complex expression \((3x + 5i)^2\), we can use the formula for squaring a binomial, which is \((a + b)^2 = a^2 + 2ab + b^2\).

Here, \(a = 3x\) and \(b = 5i\).

Now let's calculate:

  1. \(a^2 = (3x)^2 = 9x^2\)
  2. \(b^2 = (5i)^2 = 25i^2\) (Since \(i^2 = -1\), this becomes \(25(-1) = -25\))
  3. \(2ab = 2(3x)(5i) = 30xi\)

Now, combine these results:

\[ (3x + 5i)^2 = 9x^2 + 30xi - 25 \]

Thus, we can rewrite the expression as:

\[ (3x + 5i)^2 = 9x^2 + 30xi - 25 \]

This is an equivalent expression for \((3x + 5i)^2\).