Convert to Trigonometric Form 3+2i

Problem

3+2*i

Solution

1. Identify the real part a=3 and the imaginary part b=2 of the complex number z=a+b*i

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

r=√(,3+2)

r=√(,9+4)

r=√(,13)

3. Determine the argument θ using the formula tan(θ)=b/a Since the point (3,2) is in the first quadrant, θ=arctan(b/a)

θ=arctan(2/3)

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

z=√(,13)*(cos(arctan(2/3))+i*sin(arctan(2/3)))

Final Answer

3+2*i=√(,13)*(cos(arctan(2/3))+i*sin(arctan(2/3)))

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