let be A=x1i+y1j B=x2i+y2j A+B=(x1+x2)i+(y1+y2)j lA+Bl^2=(x1+x2)^2+(y1+y2)^2 now lAl^2=x1^2+y1^2 lBl^2=x2^2+y2^2 and AB=x1x2+y1y2 now lAl^2+2AB+lBl^2=x1^2+x2^2+2x1x2+2y1y2+y1^2+y2^2=(x1+x2)^2+(y1+y2)^2=lA+Bl^2 there fore lA+Bl^2=lAl^2+2AB+lBl^2 or lA+Bl^2=lAl^2+lBl^2+2lAllBl=lAl^2+2AB+lBl^2 Solution let be A=x1i+y1j B=x2i+y2j A+B=(x1+x2)i+(y1+y2)j lA+Bl^2=(x1+x2)^2+(y1+y2)^2 now lAl^2=x1^2+y1^2 lBl^2=x2^2+y2^2 and AB=x1x2+y1y2 now lAl^2+2AB+lBl^2=x1^2+x2^2+2x1x2+2y1y2+y1^2+y2^2=(x1+x2)^2+(y1+y2)^2=lA+Bl^2 there fore lA+Bl^2=lAl^2+2AB+lBl^2 or lA+Bl^2=lAl^2+lBl^2+2lAllBl=lAl^2+2AB+lBl^2.

1. An S corporation is formed by filing an Articles of Incorporation with the appropriate authority..
It issues stock and the stock holders are called shareholders
Apart from its features as a corporation, it has the additional feature that it is given the status of a
pass-through entity for federal tax purposes. This status is attained on an election made with the
Internal Revenue Service.
Advantages of S corporation.
The advantages of an S corporation often outweigh any perceived disadvantages. The S
corporation structure can be especially beneficial when it comes time to transfer ownership or
discontinue the business. These advantages are typically unavailable to sole proprietorships and
general partnerships. S corporation advantages include:
The shareholders have limited liability; their liability is limited to the unpaid amount if any on
their shares. Beyond this they are not liable for the debts and obligations of the corporation. They
cannot be called upon to contribute to pay off the corporations liabilities nor is their personal
assets liable for those liabilities. This advantage is unlike a partnership in whose case the partners
have unlimited liability
An S corporation is a pass through entity for federal tax purposes. No tax is payable at the
corporate level. Its income or loss is "passed through" to the shareholders who have to include
it in their personal income. Double taxation is avoided.
Further, if the S corporation makes losses, the shareholders can set of their share of the losses of
the corporation against their personal income and pay tax on the balance. This could be an
advantageous for start up corporations who may makes losses early.
Shareholders of the S corporation can be employees of the corporation and draw the benefits
available to them as employees.
Interests in an S corporation can be freely transferred without having adverse tax consequences.
In the case of a partnership or an LLC, the transfer of more than half of the interest in the
organization can culminate in its termination.
Besides, an S corporation need not make adjustments to property basis or comply with
complicated accounting rules in the event of transfer of an ownership interest.
In contrast to a partnership or LLC, an S corporation has greater credibility with customers,
employees, suppliers and creditors as the corporate form is seen as committed entity.
Disadvantages of an S corporation.
Forming an S corporation needs greater formalities and entails fees for filing Articles of
Incorporation. Most states have imposed ongoing fees for annual report etc. Partnerships have no
such botherations.
There cannot be more than 100 shareholders which restriction will limit the fund raising ability

2. of the corporation. Foreign ownership is prohibited.
Further, there can be only one class of shares, though voting and non-voting shares can be
issued.
Because of the Pass through character in respect of federal taxation, the scrutinizes payments to
make sure the characterization of payments is real. If not, the distributions may be treated as
wages with liability to employment tax or wages may be treated as dividends whereby
deductions are denied.
As the corporation has only one-class-of-stock, it cannot allocate losses or income to specific
shareholders. It depends on stock ownership. In the case of a Partnership of LLC this can be
done through the terms of the operating agreement.
Choice of Ownership on the basis of tax obligations:
For a start-up business with less than 100 owners the S corporation is the best form. The reasons
are
Solution
An S corporation is formed by filing an Articles of Incorporation with the appropriate authority..
It issues stock and the stock holders are called shareholders
Apart from its features as a corporation, it has the additional feature that it is given the status of a
pass-through entity for federal tax purposes. This status is attained on an election made with the
Internal Revenue Service.
Advantages of S corporation.
The advantages of an S corporation often outweigh any perceived disadvantages. The S
corporation structure can be especially beneficial when it comes time to transfer ownership or
discontinue the business. These advantages are typically unavailable to sole proprietorships and
general partnerships. S corporation advantages include:
The shareholders have limited liability; their liability is limited to the unpaid amount if any on
their shares. Beyond this they are not liable for the debts and obligations of the corporation. They
cannot be called upon to contribute to pay off the corporations liabilities nor is their personal
assets liable for those liabilities. This advantage is unlike a partnership in whose case the partners
have unlimited liability
An S corporation is a pass through entity for federal tax purposes. No tax is payable at the
corporate level. Its income or loss is "passed through" to the shareholders who have to include
it in their personal income. Double taxation is avoided.
Further, if the S corporation makes losses, the shareholders can set of their share of the losses of
the corporation against their personal income and pay tax on the balance. This could be an

3. advantageous for start up corporations who may makes losses early.
Shareholders of the S corporation can be employees of the corporation and draw the benefits
available to them as employees.
Interests in an S corporation can be freely transferred without having adverse tax consequences.
In the case of a partnership or an LLC, the transfer of more than half of the interest in the
organization can culminate in its termination.
Besides, an S corporation need not make adjustments to property basis or comply with
complicated accounting rules in the event of transfer of an ownership interest.
In contrast to a partnership or LLC, an S corporation has greater credibility with customers,
employees, suppliers and creditors as the corporate form is seen as committed entity.
Disadvantages of an S corporation.
Forming an S corporation needs greater formalities and entails fees for filing Articles of
Incorporation. Most states have imposed ongoing fees for annual report etc. Partnerships have no
such botherations.
There cannot be more than 100 shareholders which restriction will limit the fund raising ability
of the corporation. Foreign ownership is prohibited.
Further, there can be only one class of shares, though voting and non-voting shares can be
issued.
Because of the Pass through character in respect of federal taxation, the scrutinizes payments to
make sure the characterization of payments is real. If not, the distributions may be treated as
wages with liability to employment tax or wages may be treated as dividends whereby
deductions are denied.
As the corporation has only one-class-of-stock, it cannot allocate losses or income to specific
shareholders. It depends on stock ownership. In the case of a Partnership of LLC this can be
done through the terms of the operating agreement.
Choice of Ownership on the basis of tax obligations:
For a start-up business with less than 100 owners the S corporation is the best form. The reasons
are