Simplifying Complex Numbers: (5  8i)  2i(2  3i)
This article will demonstrate the process of simplifying the complex expression (5  8i)  2i(2  3i) and presenting it in standard form (a + bi).
Understanding the Steps
 Distribute: Start by distributing the 2i across the second set of parentheses.
 Simplify: Combine like terms (real numbers with real numbers, and imaginary numbers with imaginary numbers).
 Standard Form: Express the final result in the standard form of a complex number (a + bi).
Simplifying the Expression

Distribute: (5  8i)  2i(2  3i) = 5  8i  4i + 6i²

Simplify: Remember that i² = 1. Substitute this value: 5  8i  4i + 6(1) = 5  8i  4i  6 Combining like terms: (5  6) + (8  4)i = 1  12i

Standard Form: The simplified expression in standard form is 1  12i.
Conclusion
By applying the rules of complex number arithmetic, we have successfully simplified the expression (5  8i)  2i(2  3i) to its standard form, 1  12i.