Convert to Trigonometric Form i^2

Problem

i2

Solution

1. Evaluate the power of the imaginary unit i By definition, i2=−1

2. Identify the complex number in standard form a+b*i Here, z=−1+0*i

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

r=√(,(−1)2+0)

r=1

4. Determine the argument θ by locating the point (−1,0) on the complex plane. The point lies on the negative real axis.

θ=π

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

1*(cos(π)+i*sin(π))

Final Answer

i2=cos(π)+i*sin(π)

Want more problems? Check here!