(5+12i)-(9i^2-6i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (5 + 12i) - (9i² - 6i)

This article will guide you through simplifying the expression (5 + 12i) - (9i² - 6i), which involves working with complex numbers.

Understanding Complex Numbers

Complex numbers are numbers of the form a + bi, where:

• a is the real part
• b is the imaginary part
• i is the imaginary unit, defined as the square root of -1 (i² = -1)

Simplifying the Expression

1. Substitute i² with -1:

   • (5 + 12i) - (9(-1) - 6i)

2. Distribute the negative sign:

   • 5 + 12i + 9 + 6i

3. Combine real and imaginary terms:

   • (5 + 9) + (12 + 6)i

4. Simplify:

   • 14 + 18i

Conclusion

Therefore, the simplified form of the expression (5 + 12i) - (9i² - 6i) is 14 + 18i. This is a complex number with a real part of 14 and an imaginary part of 18.