Question

Help !!:/
Raise the number to the indicated power and express in trigonometric notation
[2(cos118degree+ i sin 118 degree)]^4

Answer 1

much easier than it looks
take \(2^4=16\) and then multiply each angle by \(4\) i.e. \(4\times 118\)

Answer 2

more explain plz

Answer 3

e^(i x)=cos(x)+i sin(x)

Answer 4

(cos(x)+i sin(x))^n=(e^(i x))^n=e^(i n x)=cos(n x)+i sin(n x)

Answer 5

note that eashy's formulae are in radians

Answer 6

help

Answer 7

\[[2(\cos118°+ i \sin 118°)]^4\\
=[2(\cos(118°\tfrac\pi{180°})+ i\sin (118°\tfrac\pi{180°}))]^4\\
=[2e^{i(118°\tfrac\pi{180°})}]^4\\=2^4e^{4i(118°\tfrac\pi{180°})}\\
=2^4(\cos(4\times118°\tfrac\pi{180°})+ i\sin (4\times 118°\tfrac\pi{180°}))\]