cboi89

So I'm looking at a problem that says if f(z) = x+ iy and its conjugate f'(z) = x-iy are both analytical in domain D. Show that f(z) is constant.

The solution to this problem is that 1/2 [f(z) + f ' (z) ] = Re { f(z)} . And it is also analytical. So then v(x,y) = 0 and by C.R. f(z) is a constant.

BUT I'm not 100% convinced. I understand what it is saying, but how does showing that Re{ f(z) } is analytical show us that V(x,y) is zero??? The original function could be f(z) = u +iv , just because we are looking at the Re{ f(z) } doesn't mean v don't exist.

Besides it is not possible for Re{ f(z)} = u(x,y) + i( anything).

Finally according to this, can we conclude that if either the Re{ f(z) } or Im{ f(z) } is analytic, then f(z) is automatically constant??

Thanks for bearing with me up to this point.

what would the cause be?

a) he took control of Russia's capital city

b) he took control of Germany's boarder cities.

c) He signed the Treaty of Brest- Litovsk

d) He appointed a special war council

a) the loss of Ukraine for many decades.

b) the cold war between the superpowers

c) the uprising of Revolution of 1905

d) the beginning of world war II

A) Communist Leaders believed in revolution.

B) The Romanovs had ruled Russia for 300years.

C) Their Czar, or Ruler, did not meet their basic needs.

D) Russia was becoming an industrial nation.

a) most of the senators did not agree with the u.s. policy of isolationism.

b) the senate felt the treaty would limit the US independence in world affairs.

c) The senate urged greater US involvement in the league of nations.

D) many republican senators favored greater US involvement in World Affair.

A. Made strong alliance with neighboring civlization

B. They made their neighbors believe that the gods support them

C. They assigned a governor to strictly rule conquered lands.

A. They were used in many foods and medicine.

B. They came from a long way and passed through many hands.

C. They were important part of the trade in Asian goods.

D. They represent the most popular items among many chinese.

take a guess.