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To work with complex numbers, we often need to add or subtract them. Complex numbers consist of a real part and an imaginary part. For example, in the complex number \(9 + i\), 9 is the real part and \(i\) (where \(i\) is the imaginary unit representing \(\sqrt{-1}\)) is the imaginary part.

When adding or subtracting complex numbers, simply combine the real parts together and the imaginary parts together. For example, to subtract the complex number \(3 + 2i\) from \(9 + i\):

• Subtract the real parts: \(9 - 3 = 6\)
• Subtract the imaginary parts: \(i - 2i = -i\)

This results in the complex number \(6 - i\) as the final answer.

Understanding the real and imaginary parts of complex numbers is key to mastering complex arithmetic. Each complex number can be written as \(a + bi\), where \(a\) and \(b\) are real numbers:

• \(a\) is the real part
• \(bi\) is the imaginary part

For example, in the complex number \(9 + i\):

• The real part \(a = 9\)
• The imaginary part \(bi = i\) (which implies \(b = 1\))

Identifying these parts allows us to easily perform operations like addition and subtraction. For the example given in the exercise, we identify:

• The first complex number \(9 + i\)
• The second complex number \(3 + 2i\)

The standard form of a complex number is \(a + bi\), where \(a\) and \(b\) are real numbers. This form makes it easy to perform arithmetic operations and understand the number's components.

In the previous exercise, we were tasked with performing subtraction and giving the result in standard form. After identifying the real and imaginary parts:

• The real parts: \(9 - 3 = 6\)
• The imaginary parts: \(i - 2i = -i\)

Combining these parts, our final answer is \(6 - i\) in standard form.

Always ensure that your final answer for any operation involving complex numbers is presented in this format, providing clarity and uniformity.

Practice by regularly identifying and working with the real and imaginary parts to develop a deeper understanding. This will help you in handling complex numbers with ease.