Cis notation

Evaluate the multiplication of two complex numbers in cis notation:

(6 cis 120°)(4 cis 30°)

Write the result in cis and Re-Im notation.

Correct answer:

z = 12 cis 150°
R =  -10.3923
I =  6

Step-by-step explanation:

$$\begin{gathered} A=3\cdot 4=12 \\ \alpha =120+30=150{}^{\circ } \\ z=12cis150° \end{gathered}$$

$$\begin{gathered} R=Realz \\ I=Imagz \\ R=A\cdot \cos \alpha =A\cdot \cos 150°=12\cdot \cos 150°=12\cdot (-0.866025)=-10.392=-10.3923 \end{gathered}$$

$I=A\cdot \sin \alpha =A\cdot \sin 150°=12\cdot \sin 150°=12\cdot 0.5=6$

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