Write the following complex number in polar form :
`-3 sqrt(2) + 3 sqrt(2) i`

Explanation

(i) Let `z = - 3sqrt(2) + 3sqrt(2)i` Then,
`|z| = sqrt(-3sqrt(2)^(2) + (3sqrt(2))^(2)) =6`
Let `tan alpha |(Im(z))/(Re(z))| = 1 rArr alpha = (pi)/(4)`
Since the point reqresenting z lies in the second quadrant, the agrument of z is given by
`theta = pi - alpha - ((pi)/(4)) = ((3pi)/(4))`
So, the polar form of `z - 3sqrt(2)+3sqrt(2)`i si
`z=|z|(cos theta + i sin theta) = 6 (cos.(3pi)/(4) + i sin .(3pi)/(4))`