Convert to Trigonometric Form -3i

Problem

−3*i

Solution

1. Identify the complex number in the form z=a+b*i where a=0 and b=−3

2. Calculate the modulus r using the formula r=√(,a2+b2)

r=√(,0+(−3)2)

r=√(,9)

r=3

3. Determine the argument θ by identifying the position of the point (0,−3) on the complex plane.

4. Observe that the point lies on the negative imaginary axis, which corresponds to an angle of (3*π)/2 or 270

θ=(3*π)/2

5. Substitute the values of r and θ into the trigonometric form z=r*(cos(θ)+i*sin(θ))

Final Answer

−3*i=3*(cos((3*π)/2)+i*sin((3*π)/2))

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