# Chapter 7 - Section 7.7 - Complex Numbers - 7.7 Exercises - Page 491: 52

$-27+12i$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$ To simplify the given expression, $3i(4+9i) ,$ use the Distributive Property. Then use $i^2=-1$. $\bf{\text{Solution Details:}}$ Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 3i(4)+3i(9i) \\\\= 12i+27i^2 .\end{array} Since $i^2=-1,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 12i+27(-1) \\\\= 12i-27 \\\\= -27+12i .\end{array}

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