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Chapter 2: Problem 76

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.

Short Answer

Expert verified
The statement is sensible, as the addition or subtraction of complex numbers involve combining corresponding real parts and imaginary parts, which are 'like terms'.

Step by step solution

01

Understanding Complex Numbers

In mathematics, a complex number is a number of the form \(a + bi\), where \(a\) and \(b\) are real numbers, and \(i\) is the imaginary unit, which has the property \(i^2 = -1\). The \(a\) is the real part and \(bi\) is the imaginary part of the complex number.
02

Adding Complex Numbers

To add complex numbers, add the real parts together and the imaginary parts together. For instance, if complex numbers are \(3 + 4i\) and \(1 + 2i\), upon addition we get \((3+1) + (4+2)i\) which simplifies to \(4 + 6i\). So it's like combining like terms in algebra.
03

Subtracting Complex Numbers

To subtract complex numbers, subtract the real parts and the imaginary parts separately. If the complex numbers are \(3 + 4i\) and \(1 + 2i\), upon subtraction we get \((3-1) + (4-2)i\) which simplifies to \(2 + 2i\). Again, we are basically combining like terms in algebra while subtracting complex numbers.
04

Statement Assessment

The given statement 'When I add or subtract complex numbers, I am basically combining like terms.' does make sense as the addition or subtraction of complex numbers involves combining corresponding real parts and imaginary parts, which are indeed 'like terms'.

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Most popular questions from this chapter

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{2 x-9}{x-4}$$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{3 x-7}{x-2}$$

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