(−4−4i)⋅(−5−3i)

2 min read Jun 17, 2024
(−4−4i)⋅(−5−3i)

Multiplying Complex Numbers: (−4−4i)⋅(−5−3i)

This article will walk you through the process of multiplying two complex numbers: (−4−4i)⋅(−5−3i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as the square root of -1 (i² = -1).

Multiplication Process

To multiply complex numbers, we use the distributive property just like we do with real numbers:

  1. Distribute:

    • (−4−4i)⋅(−5−3i) = (−4)⋅(−5) + (−4)⋅(−3i) + (−4i)⋅(−5) + (−4i)⋅(−3i)
  2. Simplify:

    • 20 + 12i + 20i + 12i²
  3. Substitute i² with -1:

    • 20 + 12i + 20i + 12(-1)
  4. Combine real and imaginary terms:

    • (20 - 12) + (12 + 20)i
  5. Final result:

    • 8 + 32i

Conclusion

Therefore, the product of (−4−4i)⋅(−5−3i) is 8 + 32i.

This example demonstrates the straightforward process of multiplying complex numbers using the distributive property and remembering that i² = -1.

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