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Chapter 2: Problem 25

Perform the operation and write the result in standard form. $$(9-i)-(8-i)$$

Short Answer

Expert verified
The result of the operation \((9 - i) - (8 - i)\) in standard form is 1.

Step by step solution

01

Identify Complex Numbers

First, identify the complex numbers. Here we have two complex numbers. The first complex number is \(9 - i\) and the second one is \(8 - i\).
02

Subtract Real and Imaginary Parts

Next, subtract the real part of the second complex number from the real part of the first complex number, and do the same for the imaginary parts. Real part: \(9 - 8 = 1\). Imaginary part: \(-i - (-i) = 0\). The result is that the imaginary part is now canceled, because \(-i - (-i)\) equals to 0.
03

Write Result in Standard Form

Lastly, write the result in the standard form, which is \(a + bi\). Seeing as the imaginary part is zero, there won't be any \(i\) in the result. So, the final answer will be the real part alone, which is 1.

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Most popular questions from this chapter

Find the rational zeros of the polynomial function. $$f(x)=x^{3}-\frac{1}{4} x^{2}-x+\frac{1}{4}=\frac{1}{4}\left(4 x^{3}-x^{2}-4 x+1\right)$$

Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$h(x)=4 x^{2}-8 x+3$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{4}+10 x^{2}+9$$

Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-3 x^{3}-x^{2}-12 x-20\) (Hint: One factor is \(\left.x^{2}+4 .\right)\)

Find all real zeros of the function. $$f(y)=4 y^{3}+3 y^{2}+8 y+6$$
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