Convert to Trigonometric Form -2i

Problem

−2*i

Solution

1. Identify the complex number in the form z=a+b*i where a=0 and b=−2

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

r=√(,0+(−2)2)

r=√(,4)

r=2

3. Determine the argument θ by identifying the position of the point (0,−2) 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))

−2*i=2*(cos((3*π)/2)+i*sin((3*π)/2))

Final Answer

−2*i=2*(cos((3*π)/2)+i*sin((3*π)/2))

Want more problems? Check here!