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Chapter 2: Problem 43

Perform the operation and write the result in standard form. $$(6+7 i)^{2}$$

Short Answer

Expert verified
The result of squaring the given complex number \(6 + 7i\) is \(-13 + 84i\).

Step by step solution

01

Write out the operation

Express the given operation as the multiplication of the complex number \(6+7i\) by itself, like this: \((6+7i) * (6+7i)\)
02

Apply the distributive law

Next, apply the distributive law and multiply the terms from one bracket with every term in the second bracket, namely: \(6*6, 6*7i, 7i*6, 7i*7i\)
03

Perform the Multiplication

Carry out the multiplication to get the four terms from the previous step: \(36, 42i, 42i, -49\) because \(i^2\) equals -1 in the last term \(7i*7i\).
04

Combine Like Terms

Next, combine the like terms, the real numbers and the imaginary numbers separately. This leads to: \(36 - 49 + 42i + 42i\) = \(-13 + 84i\)

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