-(3-7i)-in-standard-form.jpeg "(12+4i)-(3-7i) In Standard Form")
Simplifying Complex Numbers
This article will guide you through the process of simplifying the complex number expression (12 + 4i) - (3 - 7i) and expressing it in standard form.
Understanding Complex Numbers
A complex number is a number 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
To simplify the expression (12 + 4i) - (3 - 7i), we follow these steps:
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Distribute the negative sign: (12 + 4i) + (-1 * 3) + (-1 * -7i)
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Simplify the expression: 12 + 4i - 3 + 7i
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Combine real and imaginary terms: (12 - 3) + (4 + 7)i
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Final answer in standard form: 9 + 11i
Standard Form
The standard form of a complex number is a + bi, where 'a' is the real part and 'b' is the imaginary part. In our simplified expression, 9 + 11i, the real part is 9 and the imaginary part is 11.
Therefore, the simplified expression (12 + 4i) - (3 - 7i) in standard form is 9 + 11i.