Let y and v(x, y) = x' – 3xy² . Sho functions but that their product uv is not harmonic. 4. Show that u(x, y) = 2x-x+3xy is harmonic and f v(x, y). 5. Show that exp(z) s exp(z|") for all ze C. 6. Show...

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Extracted text: Let y and v(x, y) = x' – 3xy² . Sho functions but that their product uv is not harmonic. 4. Show that u(x, y) = 2x-x+3xy is harmonic and f v(x, y). 5. Show that exp(z) s exp(z|") for all ze C. 6. Show that Log[(-1+i)*]#2Log(-1+i). 7. Find all roots of the equation log(z) = ri / 2 8. Find the principal value of (1+ i)'. 9. Use the definitions of sin(z) and cos(z) given in Lect IT = cos(z) for all ze C. prove that sin z+- (Do not use any other trigonometry identities for que Evaluate [(3t – i)² dt 10.