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Chapter 2: Problem 13

Find each product and write the result in standard form. $$(7-5 i)(-2-3 i)$$

Short Answer

Expert verified
The product of \( (7-5 i)(-2-3 i) \) in standard form is \( 1 - 11i \).

Step by step solution

01

- Distribute real and imaginary parts

Distribute across each term within the first bracket, to each term in the second bracket. This gives: \( (7 * -2) + (7 * -3i) + (-5i* -2) + (-5i * -3i) \).
02

- Simplify terms

After distribution, simplify the terms. It will become: \( -14 - 21i + 10i + 15 \).
03

- Combine like terms

Combine the like terms, real numbers with real numbers and complex numbers with complex numbers. That will give: \( -14 + 15 + (-21i + 10i) \). This simplifies to: \( 1 - 11i \).

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Most popular questions from this chapter

Use inspection to describe each inequality's solution set. Do not solve any of the inequalities. $$\frac{1}{(x-2)^{2}}>0$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$h(x)=\frac{1}{x}+2$$

Find the horizontal asymptote, if there is one, of the graph of rational function. $$g(x)=\frac{15 x^{2}}{3 x^{2}+1}$$

Will help you prepare for the material covered in the next section. Solve: \(2 x^{2}+x=15\)

Solve each inequality using a graphing utility. $$x^{2}+3 x-10>0$$
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