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CHAPTER 12 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

${(\sqrt{- 9})}^{2} = 9$
$\frac{1 + j}{1 - j} = j$
$4/90 ° = 4 j$
$2 e^{π j} = - 2$
${(2 ∠ \underline{120^{\circ}})}^{3} = 8$
The phase angle $ϕ$ for an impedance $Z = 4 - 4 j$ is $45 °$ .

PRACTICE AND APPLICATIONS

In Exercises 7–20, perform the indicated operations, expressing all answers in simplest rectangular form.

$(6 - 2 j) + (4 + j)$
$(12 + 7 j) + (- 8 + 6 j)$
$(18 - 3 j) - (12 - 5 j)$
$(- 4 - 2 j) - \sqrt{- 49}$
$5 j (6 - 5 j)$
$- 3 j (4 - 7 j)$
$(6 - 3 j) (4 + 3 j)$
$(4 - 9 j) (1 + 2 j)$
$\frac{3}{7 - 6 j}$
$\frac{48 j}{4 + 18 j}$
$\frac{6 - \sqrt{- 16}}{\sqrt{- 4}}$
$\frac{3 + \sqrt{- 4}}{4 - j}$
$\frac{5 j - (3 - j)}{4 - 2 j}$
$\frac{2 - (6 - j)}{1 - 2 j}$

In Exercises 21–24, find the values of x and y for which the equations are valid.

$3 x - 2 j = y j$

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