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Sagot :
Using Euler's Formula:
[tex]re^{i\theta}=r(\cos (\theta)+i\sin (\theta))[/tex]Since:
[tex]\begin{gathered} z1=9(\cos (225)+i\sin (225)) \\ z2=3(\cos (45)+i\sin (45)) \\ \end{gathered}[/tex]We can rewrite them as:
[tex]\begin{gathered} z1=9e^{225i} \\ z2=3e^{45i} \end{gathered}[/tex]So:
[tex]\begin{gathered} z1\times z2=(9e^{225i})(3e^{45i})=27e^{225i+45i}=27e^{270i} \\ so\colon \\ z1\times z2=27(\cos (270)+i\sin (270)) \end{gathered}[/tex][tex]\begin{gathered} a=r\cos (\theta) \\ b=r\sin (\theta) \\ where \\ r=27 \\ \theta=270 \end{gathered}[/tex]So:
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