Find the product of z1=2/3(cos 60 degrees+i sin 60 degrees) and where 0less than equal to theta less than 360 degrees . (1 point)
To find the product of z1 and z2, we multiply the magnitudes and add the angles:
z1 = 2/3(cos 60° + i sin 60°)
To find the magnitude of z1:
|z1| = 2/3
To find the angle of z1:
θ1 = 60°
Therefore, z1 can be represented as 2/3 cis 60°.
Now, to find the product:
z1 * z2 = (2/3)(cos 60° + i sin 60°)(cos θ + i sin θ)
= (2/3)[cos 60° * cos θ - sin 60° * sin θ + i(sin 60° * cos θ + cos 60° * sin θ)]
= (2/3)[cos(60° + θ) + i sin(60° + θ)]
So, the product of z1 and z2 is 2/3 cis (60° + θ).