(10i-4i^2)-(7-3i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Numbers: (10i - 4i²) - (7 - 3i)

This article will guide you through the steps involved in simplifying the complex number expression: (10i - 4i²) - (7 - 3i).

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where:

• a is the real part, and
• b is the imaginary part.
• i is the imaginary unit, where i² = -1.

Simplifying the Expression

1. Simplify the i² term:

   • Remember that i² = -1. Substitute this value into the expression: (10i - 4(-1)) - (7 - 3i)

2. Distribute the negative sign:

   • (10i + 4) - (7 - 3i)

3. Combine like terms:

   • (4 - 7) + (10i + 3i)

4. Simplify:

   • -3 + 13i

Conclusion

Therefore, the simplified form of the complex number expression (10i - 4i²) - (7 - 3i) is -3 + 13i.