How do you multiply and simplify the product of 3, 5i, 2, and 4i?

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To multiply and simplify the expression involving the numbers 3, 5i, 2, and 4i, you can follow these steps:

  1. Group the terms: Start by rearranging the expression for clarity:
    • (3 * 2) * (5i * 4i)
  2. Multiply the real numbers: First, multiply the real components:
    • 3 * 2 = 6
  3. Multiply the imaginary numbers: Next, handle the imaginary part:
    • 5i * 4i = 20i2
  4. Substitute the value of i2: Remember that i2 = -1:
    • 20i2 = 20(-1) = -20
  5. Add the results: Now, combine the results from the real and imaginary parts:
    • 6 – 20 = -14

Therefore, the simplified product of 3, 5i, 2, and 4i is:

-14

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