Convert to Trigonometric Form i^8

Problem

i8

Solution

1. Simplify the expression using the properties of the imaginary unit i

i8=(i4)2

i8=(1)2=1

2. Identify the real and imaginary parts of the simplified number.

z=1+0*i

3. Calculate the modulus r of the complex number.

r=√(,1+0)=1

4. Determine the argument θ by finding the angle on the unit circle where the real part is 1 and the imaginary part is 0

cos(θ)=1

sin(θ)=0

θ=0

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

1*(cos(0)+i*sin(0))

Final Answer

i8=cos(0)+i*sin(0)

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