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 $z=r(cos\theta +isin\theta )$.

Step 6 ：Step 6: So, $-3+4i=5(cos2.2142974+isin2.2142974)$.