The modulus (absolute value) of \(z\) is found by taking the square root of the sum of the squares 0f its components, thus \(| z | = 3\sqrt{2}\).
The angle \(t=\arg z\) is the standard radian angle with terminal side through the point \(( 3, 3 )\), that is, \(t=\frac{\pi}{4}\).
Thus, the trigonometric form for the complex number \(3 + 3 i\) is \(3\sqrt{2} \left( \cos \frac{\pi}{4} + i \sin \frac{\pi}{4}\right)\).