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

less than a minute read Jun 16, 2024
(10i-4i^2)-(7-3i)

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.

Related Post