Answer
$$ - \frac{{15\sqrt 2 }}{2} + \frac{{15\sqrt 2 }}{2}i$$
Work Step by Step
$$\eqalign{
& \left( {5\operatorname{cis} {{90}^ \circ }} \right)\left( {3\operatorname{cis} {{45}^ \circ }} \right) \cr
& {\text{Multiply using the Product Theorem}} \cr
& = \left( 5 \right)\left( 3 \right)\operatorname{cis} \left( {{{90}^ \circ } + {{45}^ \circ }} \right) \cr
& {\text{Simplify}} \cr
& = 15\operatorname{cis} \left( {{{135}^ \circ }} \right) \cr
& = 15\left( {\cos {{135}^ \circ } + i\sin {{135}^ \circ }} \right) \cr
& {\text{Write in Rectangular form}} \cr
& = 15\left( { - \frac{{\sqrt 2 }}{2} + \frac{{\sqrt 2 }}{2}i} \right) \cr
& = - \frac{{15\sqrt 2 }}{2} + \frac{{15\sqrt 2 }}{2}i \cr} $$
