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Complex numbers are comprised of two components: the real part and the imaginary part. The real part of a complex number is the numeric term not linked to the imaginary unit \(i\). In comparison, the imaginary part is linked to \(i\), which signifies the square root of -1.
For a complex number expressed as \(a + bi\), \(a\) is acknowledged as the real part and \(bi\) signifies the imaginary part. To comprehend this better, consider the example \(-14 + 17i\). Here, the real part is \(-14\), and the imaginary part is \(17i\). It is crucial to distinguish these parts when working with complex numbers as each plays a unique role in arithmetic operations, such as addition and subtraction of complex numbers.

Combining like terms is a fundamental concept in algebra, including when working with complex numbers. Like terms possess identical variables raised to the same power or, in the case of complex numbers, terms that either share the real part or the imaginary part.
In the expression \(8i - 14 + 9i\), we identify like terms by looking for terms with the imaginary unit \(i\), such as \(8i\) and \(9i\). These are combined through addition or subtraction. By combining, we get \(8i + 9i = 17i\). The real term \(-14\) is not combined with any other term in this example as there is no other like term. Understanding how to combine like terms is crucial for simplifying complex number expressions.

The standard form of a complex number is expressed as \(a + bi\), where \(a\) is the real part and \(b\) corresponds to the magnitude of the imaginary part attached to the imaginary unit \(i\).
Representing a complex number in this way ensures consistent and straightforward calculations when performing arithmetic operations. Following our exercise, after distributing the negative sign and combining like terms, the complex number \(-14 + 17i\) emerges.
In this format, it is clear to see both components of the complex number, allowing for better interpretation and easier continuation in subsequent mathematical calculations. Recognizing and writing complex numbers in standard form enables clear communication and understanding in complex number arithmetic.