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(9-7i)(1+3i)-2(3-4i)

less than a minute read Jun 16, 2024
(9-7i)(1+3i)-2(3-4i)

Simplifying Complex Expressions: (9-7i)(1+3i) - 2(3-4i)

This article will guide you through the steps of simplifying the complex expression: (9-7i)(1+3i) - 2(3-4i).

Understanding Complex Numbers

Complex numbers are numbers of the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit, where i² = -1.

Simplifying the Expression

  1. Expand the product:

    • (9-7i)(1+3i) = (9 * 1) + (9 * 3i) + (-7i * 1) + (-7i * 3i)
    • = 9 + 27i - 7i - 21i²

  2. Simplify using i² = -1:

    • = 9 + 27i - 7i + 21

  3. Combine real and imaginary terms:

    • = (9 + 21) + (27 - 7)i
    • = 30 + 20i

  4. Simplify the second part of the expression:

    • -2(3-4i) = -6 + 8i

  5. Combine the simplified parts:

    • (30 + 20i) + (-6 + 8i) = 24 + 28i

Final Result

Therefore, the simplified form of (9-7i)(1+3i) - 2(3-4i) is 24 + 28i.

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