A student has a lesson on Complex Numbers and makes the following conclusions:

- \(\mathbb{R} \subset \mathbb{I}\)
- \(\mathbb{I} \subset \mathbb{C}\)
- \(\sqrt[-1]{-i} = i\)
- \(\sqrt[]{\bar{z}z} = |z|\)
- \(z = r\cos(\theta)+ir\sin(\theta)\)

Which of the above is/are **false**?

**Notes:**

- \(i = \sqrt {-1}\) is the imaginary unit
- \(\mathbb{R}\) is the set of all real numbers
- \( \mathbb{I}\) is the set of all imaginary numbers
- \( \mathbb{C}\) is the set of all complex numbers
- \(z=a+ ib; a,b \in \mathbb R\) is the general form of a complex number
- \(\bar{z} = a-ib\) is the conjugate of \(z\)
- \(|z| = \sqrt{a^2+b^2}\) is the modulus of \(z\)

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