Problem 70 - Algebra and Trigonometry

Question

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When I add or subtract complex numbers, I am basically combining like terms.

Step-by-Step Solution

Answer

The statement makes sense based on the principles of combining 'like terms' and addition/subtraction operations of complex numbers.

Step 1: Understanding Like Terms

Like terms are terms that contain same variables and powers. In simple words, terms that are 'similar' can be added or subtracted. An example in algebra can be adding \(2x\) and \(3x\) to get \(5x\)

Step 2: Understanding Complex Numbers

A complex number has a form \(a + bi\) where \(a\) and \(b\) are real numbers and \(i\) is the imaginary unit, which is defined by \(i^2 = -1\). In a complex number, \(a\) is the real part and \(bi\) is the imaginary part.

Step 3: Adding/Subtracting Complex Numbers

When adding or subtracting complex numbers, we combine the real parts with the real parts and the imaginary parts with the imaginary parts. For example, if we have two complex numbers, \(a+bi\) and \(c+di\), we can add them together to get \((a+c) + (b+d)i\). Similarly, subtraction would lead to \((a-c) + (b-d)i\). So, we can consider the real and imaginary parts as 'like terms'.

Step 4: Conclusion on the argument

Considering the above explanation, the original statement 'When I add or subtract complex numbers, I am basically combining like terms' indeed makes sense. The real parts and the imaginary parts of complex numbers can be considered as 'like terms'. They are combined together during addition or subtraction.