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Chapter 2: Problem 52

Perform the indicated operation(s) and write the result in standard form. $$(8+9 i)(2-i)-(1-i)(1+i)$$

Short Answer

Expert verified
The result of the operation in standard form is \(25 + 10i\).

Step by step solution

01

Simplify the multiplication operations

Apply the distributive property and perform the multiplication operations. From \((8+9i)(2-i)\) we get the product \(16 - 8i + 18i - 9i^2\), and from \((1-i)(1+i)\) we get the product \(1 - i + i - i^2\).
02

Substitute \(i^2\) with \(-1\)

Replace \(i^2\) with \(-1\). Our expressions become \(16 - 8i + 18i + 9\) and \(1 - 1\), which then simplify to \(25 + 10i\) and \(0\), respectively.
03

Perform the subtraction operation

Subtract the second result from the first, which leaves us with \(25 + 10i - 0 = 25 + 10i\).

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Most popular questions from this chapter

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

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