(1+7i)(9+3i)-(4+2i)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions: (1+7i)(9+3i)-(4+2i)

This article will guide you through the process of simplifying the complex expression: (1+7i)(9+3i)-(4+2i).

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).

Steps to Simplify the Expression

1. Expand the product:

   • (1+7i)(9+3i) = 1(9) + 1(3i) + 7i(9) + 7i(3i)
   • = 9 + 3i + 63i + 21i²
   • = 9 + 66i + 21(-1) (Since i² = -1)
   • = -12 + 66i

2. Combine the expanded product with the remaining term:

   • (-12 + 66i) - (4 + 2i)
   • = -12 - 4 + 66i - 2i
   • = -16 + 64i

Final Result

Therefore, the simplified form of the expression (1+7i)(9+3i)-(4+2i) is -16 + 64i.