%2B(7%2B3i)-in-standard-form.jpeg "(6-i)+(7+3i) In Standard Form")
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
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Group the real and imaginary terms:
(6 - i) + (7 + 3i) = (6 + 7) + (-1 + 3)i
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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.