Question

if f(z)=u+iv and u-v=ex(cos y-sin y) find f(z)

Answer 1

Answer:

Step-by-step explanation: Take u = eˣ cos y and v = eˣsin y

then,

f (z)= u + iv

f(z) = eˣ cos y + eˣ sin y

f(z) = eˣ (cos y =i sin y)

f(z) = eˣ e(iy), ( Euler 's identity )

f(z) = e ^(x+ iy)

f(z) = e^z

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