(7+2i)(9-6i)

2 min read Jun 16, 2024
(7+2i)(9-6i)

Multiplying Complex Numbers: (7 + 2i)(9 - 6i)

This article will demonstrate how to multiply two complex numbers: (7 + 2i) and (9 - 6i).

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, similar to how we multiply binomials:

  1. Expand the product: (7 + 2i)(9 - 6i) = 7(9 - 6i) + 2i(9 - 6i)

  2. Distribute: = 63 - 42i + 18i - 12i²

  3. Simplify by substituting i² with -1: = 63 - 42i + 18i + 12

  4. Combine real and imaginary terms: = (63 + 12) + (-42 + 18)i

  5. Final Result: = 75 - 24i

Therefore, the product of (7 + 2i) and (9 - 6i) is 75 - 24i.

Conclusion

Multiplying complex numbers involves applying the distributive property and simplifying by substituting i² with -1. This process results in a new complex number, expressed in the standard form a + bi.

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