Answer:
[tex]16\sqrt[3]{-1}[/tex]
Step-by-step explanation:
Given complex numbers:
z1 = 8(cos20° + isin20°)
z2 = 2(cos40° + i sin40°)
z1.z2 = 8(cos20° + isin20°) * 2(cos40° + i sin40°)
Converting degree to radians:
8(cos(π/9) + isin(π/9)) * 2(cos(2π/9) + i sin(2π/9))
Use the following identity:
[tex]cos(x)+isin(x)=e^{ix}[/tex]
8(cos(π/9) + isin(π/9)) * 2(cos(2π/9) + i sin(2π/9)) will become:
[tex]2*8e^{i\frac{2pi}{9} } e^{i\frac{pi}{9}}[/tex]
= [tex]16\sqrt[3]{-1}[/tex]
