3. Recall that z = x+iy. For each of the given functions, use a result related to the Cauchy- Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it exists, find its value according to the theorem. (i) f(2)=2x+ixy² (ii) g(z) = x³ +iy³ (iii) h(z)= 2²-²

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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105.
3. Recall that z = 2+iy. For each of the given functions, use a result related to the Cauchy-
Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it
exists, find its value according to the theorem.
(i) f(2)=2x+ixy²
(ii) g(z) = x³ + iy³
(iii) h(2) = 2²-²
(iv) k(z)= ¢ *sin r – ie M cos r
Transcribed Image Text:3. Recall that z = 2+iy. For each of the given functions, use a result related to the Cauchy- Riemann Equations (sections 21, 23, or 24) to determine where the derivative exists. If it exists, find its value according to the theorem. (i) f(2)=2x+ixy² (ii) g(z) = x³ + iy³ (iii) h(2) = 2²-² (iv) k(z)= ¢ *sin r – ie M cos r
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