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Chapter 2: Problem 36

Perform the operation and write the result in standard form. $$-8 i(9+4 i)$$

Short Answer

Expert verified
The result of the operation is \(32 -72i\)

Step by step solution

01

Distributive Property

Apply distributive property to multiply -8i with both terms inside the bracket, which means multiply -8i with 9 and with \(4i\): \[-8i*9,-8i*4i\]
02

Performing the Multiplication

Perform the multiplication: \[-72i, -32i^{2}\]
03

Simplifying the product

Using the fact that \(i^{2} = -1\), replace \(i^{2}\) in the second term with -1: \[-72i, -32*-1\] which becomes \[-72i, 32\]
04

Obtaining the final result

Sum up both results, the real part comes first and then the imaginary part. So our final result is \(32 -72i\)

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