Simplifying Complex Numbers: (6  i) + (7 + 3i)
This article will guide you through the process of simplifying the expression (6  i) + (7 + 3i) and presenting it in standard form.
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.
Simplifying the Expression

Group the real and imaginary terms:
(6  i) + (7 + 3i) = (6 + 7) + (1 + 3)i

Combine like terms:
(6 + 7) + (1 + 3)i = 13 + 2i
Standard Form
The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part. Therefore, the simplified expression (6  i) + (7 + 3i) = 13 + 2i is in standard form.
Conclusion
We successfully simplified the expression (6  i) + (7 + 3i) and expressed it in standard form as 13 + 2i. This process demonstrates how to manipulate complex numbers by combining real and imaginary terms, resulting in a simplified expression in standard form.