If `i=sqrt(-1)` then `(cos(pi/3)+i sin(pi/3))^3=`

z=(1-i)/(cos(pi/3)+i sin(pi/3))

If z_(1) = sqrt(2)(cos""(pi)/(4) + "" i sin""(pi)/(4)) and z_(2) = sqrt(3)(cos""(pi)/(3) + i sin""(pi)/(3)) , then |z_(1)z_(2)| is

Express the following numbers in the form x + iy. sqrt(3)(cos (pi / 6) + i sin (pi / 6))

"statement-1" (cos theta+isin theta)^(3)=cos 3theta+isin 3theta, i=sqrt(-1) bb"statement-2" (cos""pi/4+isin""pi/4)^(2)=i

Prove that (i)(1-sqrt(3)i)=2((cos)(pi)/(3)-i(sin)(pi)/(3))

If z_(1)=sqrt(2)((cos pi)/(4)+i sin((pi)/(4))) and z_(2)=sqrt(3)((cos pi)/(3)+i sin((pi)/(3))) then |z_(1)z_(2)|=

Two of the three value of (-1)^((1)/(3)) are cos((pi)/(3))+i sin((pi)/(3)) and cos((5 pi)/(3))+i sin((5 pi)/(3)) the third value is

5.The modulus amplitude form of -1-i is (a) -sqrt(2)(cos(pi/4)+i sin(pi/4)) (b) sqrt(2)(cos((3pi)/4)+i sin((3pi)/4)) (c) sqrt(2)[cos(-(3 pi)/(4))+i sin(-(3 pi)/(4))] (d) None of these.

The numerical value of (where i = sqrt-1 ) (cos pi/10 + i sin pi/10)(cos 2pi/10 + i sin 2pi/10) xx (cos 3pi/10 + i sin 3pi/10) (cos 4pi/10 + i sin 4pi/10) = ..........