Prove that (i) `(1-sqrt3i) = 2((cos) pi/3-i (sin)pi/3)`

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

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

Prove that (i) " sin " .(pi)/(6). " cos " .(pi)/(6) = (sqrt(3))/(4) " " (iii) cos^(2) .(pi)/(2) - sin^(2) .(pi)/(2) =(sqrt(3))/(2)

Prove that (i) "sin " (7pi)/(12) " cos " (pi)/(2) - "cos " *(7pi)/(12) " sin " (pi)/(4) = (sqrt(3))/(2) (ii) " sin " (pi)/(4) " cos " (pi)/(2) + "cos"(pi)/(4) " sin " (pi)/(12) = (sqrt(3))/(2) (iii) " cos " (2pi)/(3) " cos " (pi)/(4) - " sin " (2pi)/(3) " sin " (pi)/(4) =(-(sqrt(3) +1))/(2sqrt(2))

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

Prove that (i) " 2sin " (5pi)/(12) " sin " (pi)/(12)=(1)/(2) (ii) " 2 cos " (5pi)/(12) " cos " .(pi)/(12)=(1)/(2) (iii) " 2 sin ".(5pi)/(12) " cos " (pi)/(2) = ((2+sqrt(3))/(2))

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

Write the complex number z = (i-1)/(cos pi/3 + i sin pi/3) in polar form.

Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the polar form.