Convert to Trigonometric Form -4i

Problem

−4*i

Solution

1. Identify the complex number in the form z=a+b*i where a=0 and b=−4

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

r=√(,0+(−4)2)

r=√(,16)

r=4

3. Determine the argument θ by identifying the position of the point (0,−4) on the complex plane.

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

θ=(3*π)/2

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

−4*i=4*(cos((3*π)/2)+i*sin((3*π)/2))

Final Answer

−4*i=4*(cos((3*π)/2)+i*sin((3*π)/2))

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