Express the complex number \(z = -3 + 4i\) in trigonometric form.

Step 1 ：Step 1: Compute the modulus (r) of the complex number. The formula for r is \(r = \sqrt{a^2 + b^2}\) where a is the real part and b is the imaginary part of the complex number. Here, a is -3 and b is 4.

Step 2 ：Step 2: Use the formula \(r = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5\) to compute the modulus.

Step 3 ：Step 3: Compute the argument (\(\theta\)) of the complex number. The formula for \(\theta\) is \(\theta = atan2(b, a)\) Here, a is -3 and b is 4.

Step 4 ：Step 4: Use the formula \(\theta = atan2(4, -3)\) to compute the argument. We find that \(\theta\) is approximately 2.2142974.

Step 5 ：Step 5: Finally, the trigonometric form of the complex number is \(z = r(cos \theta + i sin \theta)\).

Step 6 ：Step 6: So, \(-3 + 4i = 5(cos 2.2142974 + i sin 2.2142974)\).