If a = cos(alpha) +i sin(alpha), b = cos(beta) +i sin(beta), c= cos(gamma) + i sin(gamma) and a+b+c = 0, then what is the value of a-1 +b-1+c-1? Share with your friends Share 9 Akhil Goyal answered this Given:cosα+cosβ+cosγ+isinα+sinβ+sinγ=0+i0⇒cosα+cosβ+cosγ=0 ---(1)and, sinα+sinβ+sinγ=0 ---(2)a=cosα+isinαalso, a¯=cosα-isinαa-1=1cosα+isinαmultplying by a¯ in numerator and denominator:a-1=cosα-isinαa2 (since a·a=a2)⇒a-1=cosα-isinαcos2α+sin2α=cosα-isinα (since cos2α+sin2α)Similarly, we will have:b-1=cosβ-isinβand,c-1=cosγ-isinγTherefore:a-1+b-1+c-1=cosα+cosβ+cosγ-isinα+sinβ+sinγUsing (1) and (2):a-1+b-1+c-1==0 9 View Full Answer