How can you use trigonometric functions to simplify # 8 e^( ( 2 pi)/3 i ) # into a non-exponential complex number?
1 Answer
May 26, 2016
Explanation:
Using
#color(blue)"Euler's identity"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(re^(thetai)=r(costheta+isintheta))color(white)(a/a)|)))# here r = 8 and
#theta=(2pi)/3#
#rArr8e^((2pi)/3i)=8(cos((2pi)/3)+isin((2pi)/3))#
#=8(-1/2+(sqrt3)/2 i)=-4+4sqrt3 i#
