Let f be an analytic function in C. Assume that f satisfies f(z + 2Ï) = f(z), f(z + 2Ïi) = f(z), for all z â C. Show that f is constant.
Let ⦠â C be a domain and f : ⦠â C be analytic. Assume that the function cos(f(z)) is constant. Show that f is constant.
Sample Solution
Comfort Each duty ought to be required in such a way and at such a period, that it gives the citizen most extreme comfort. Assessment in the UK is commonly gathered by either taking from the citizen before they get the remainder of the cash, referred to as the Pay As You Earn (PAYE) framework, or they pay it straightforwardly to the administration (HMRC). Economy The expense of gathering assessment ought to be the base with the goal that a significant piece of assortment is towards the treasury. In the event that organization costs expends an enormous part of duty income, it can’t be said it is a decent assessment framework. Duty frameworks change far and wide because of recorded and institutional contrasts, yet any great framework must look for the least total penance in its assessment strategies. For 2018, the UK government burned through 2% of their complete spending on general government where HMRC is incorporated (Chantrill, 2019). Additional Characteristics Effortlessness Expense ought to be easy to such an extent that any citizen can comprehend its calculation and difficulties without the assistance of a specialist. It would likewise decrease the opportunity of tax avoidance as it won’t trouble the person to make good on charge. A straightforward assessment framework is likewise gainful for the legislature because of investing less energy and cash. A duty framework that treats comparative financial exercises in comparative manners for charge purposes will in general be more straightforward and dodge separation among individuals and monetary exercises. Anyway it can now and again be effective to separate between various exercises for charge purposes, for example, UK imposes on liquor and tobacco, and different things that hurt others and the earth.>
Comfort Each duty ought to be required in such a way and at such a period, that it gives the citizen most extreme comfort. Assessment in the UK is commonly gathered by either taking from the citizen before they get the remainder of the cash, referred to as the Pay As You Earn (PAYE) framework, or they pay it straightforwardly to the administration (HMRC). Economy The expense of gathering assessment ought to be the base with the goal that a significant piece of assortment is towards the treasury. In the event that organization costs expends an enormous part of duty income, it can’t be said it is a decent assessment framework. Duty frameworks change far and wide because of recorded and institutional contrasts, yet any great framework must look for the least total penance in its assessment strategies. For 2018, the UK government burned through 2% of their complete spending on general government where HMRC is incorporated (Chantrill, 2019). Additional Characteristics Effortlessness Expense ought to be easy to such an extent that any citizen can comprehend its calculation and difficulties without the assistance of a specialist. It would likewise decrease the opportunity of tax avoidance as it won’t trouble the person to make good on charge. A straightforward assessment framework is likewise gainful for the legislature because of investing less energy and cash. A duty framework that treats comparative financial exercises in comparative manners for charge purposes will in general be more straightforward and dodge separation among individuals and monetary exercises. Anyway it can now and again be effective to separate between various exercises for charge purposes, for example, UK imposes on liquor and tobacco, and different things that hurt others and the earth.>
