Can someone help me with this? Put into trigometric form: -2+2sqrt3i= ___(cos(___)+isin(___))
Note that | -2 + 2sqrt(3)i | = sqrt{ (-2)^2 + (2sqrt3)^2 } = sqrt{ 4 + 12 } = sqrt( 16 ) = 4. Therefore, factoring out a 4, we have -2 + 2sqrt(3)i = 4 * ( -1/2 + sqrt(3)/2 i ) Now the angle t that gives cos(t) = -1/2 sin(t) = sqrt(3)/2 is t = 2pi/3. Therefore, we conclude -2 + 2sqrt(3)i = 4 * ( cos(2pi/3) + i sin(2pi/3) ).