What is the complex number z=−3+3i represented in polar form? Enter the angle measure as the smallest positive angle in simplified form and any radicals in simplified form.
z = -3 + 3i
To find the value of r: r = sqrt( (-3)2 + (3)2 ) = sqrt( 9 + 9 ) = sqrt(18) = 3sqrt(2)
To find the angle: tan-1( 3 / -3 ) = tan-1( -1 ) = 3pi / 4 [remember that it is in the second quadrant]
3sqrt(2) cis( 3pi/4)