3. 设u=(x^3+y^3)/(x^2+y^2) ,z≠0,
f(z)=u+iu .,z≠0,
du/dx=du/dy; du/dx/-du/dy=0 满足R-C 条件,f(z)在z=0间断,不可微
4设.f(z)=u+iv
(1)v=0, R-C condition ==>du/dx=du/dy=0, u=常数
(2)f(z),f('(z)解析,f'(z)=du/dx+idv/dx
f'(z)=du/dy-idu/dy
R-C 条件 ==>f(z)=常数
(3)u=常数, R-C 条件 ==>v=常数
5. z=x+iy
z^2=x^2+2ixy-y^2
x z^2=x^3-x(y^2) +2ix^2 y ==>x(y^2)不能是唯一实数
6.
exp(ix)=cos(x)+isin(x)
sinx=(1/2)i(exp(ix)-exp(-ix))
cosx=(1/2)i(exp(ix)+exp(-ix))
sinhx=(1/2)(exp(x)-exp(-x))
coshx=(1/2)(exp(x)+exp(-x))...
7.
lim(z->z0) f(z)/g(z)=lim(z->z0) [f(z)-f(z0)]/[g(z)-g(z0)]
=lim(z->z0) {[f(z)-f(z0)]/[g(z)-g(z0)]}=f'(z0)/g'(z0)
8.
Lim [sin(u+iv)]/(u+iv)=lim (u->0,v->0)cos(u+iv)=lim (u->0,v->0)[cosu cosiv-sinu siniv]=1