Convert to Trigonometric Form i

Problem

i

Solution

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

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

r=√(,0+1)

r=1

3. Determine the argument θ by finding the angle in the complex plane where the point (0,1) lies.

cos(θ)=a/r=0/1=0

sin(θ)=b/r=1/1=1

θ=π/2

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

z=1*(cos(π/2)+i*sin(π/2))

Final Answer

i=cos(π/2)+i*sin(π/2)

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