taylors1mommie
taylors1mommie taylors1mommie
  • 22-02-2019
  • Mathematics
contestada

Find the product of the given complex numbers. z1 = 8(cos20° + isin20°) z2 = 2(cos40° + i sin40°)

Respuesta :

SaniShahbaz
SaniShahbaz SaniShahbaz
  • 22-02-2019

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]

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