Question

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

Answer 1

`16\sqrt[3]{-1}`

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:

`cos(x)+isin(x)=e^(ix)`

8(cos(π/9) + isin(π/9)) * 2(cos(2π/9) + i sin(2π/9)) will become:

`2*8e^{i(2pi)/(9) } e^{i(pi)/(9)}`

=
`16\sqrt[3]{-1}`