2. Prove, for instance, that 3 < π < 2√3.
4. For what values of z is eᶻ equal to 2, -1, i, -i/2, -1-i, 1+2i ?
8. Express arc tan w in terms of the logarithm.

1. Find the values of sin i, cos i, tan(1 + i).
2. The hyperbolic cosine and sine are defined by cosh z = (eᶻ + e⁻ᶻ)/2, sinh z = (eᶻ - e⁻ᶻ)/2. Express them through cos iz, sin iz. Derive the addition formulas, and formulas for cosh 2z, sinh 2z.
3. Use the addition formulas to separate cos(x + iy), sin(x + iy) in real and imaginary parts.

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