Convert to Trigonometric Form 2+2i

Problem

2+2*i

Solution

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

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

r=√(,2+2)

r=√(,4+4)

r=√(,8)

r=2√(,2)

3. Determine the argument θ using the formula tan(θ)=b/a

tan(θ)=2/2

tan(θ)=1

4. Find the angle θ in the first quadrant since both a and b are positive.

θ=π/4

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

z=2√(,2)*(cos(π/4)+i*sin(π/4))

Final Answer

2+2*i=2√(,2)*(cos(π/4)+i*sin(π/4))

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