Article: When you want to divide two complex numbers, set up the problem as a fraction. For example, to find the quotient of (4+3i) divided by (2-2i), set up the problem as follows: (4+3i)(2−2i){\displaystyle {\frac {(4+3i)}{(2-2i)}}} The conjugate of a complex number is a useful tool. It is simply created by changing the sign in the middle of the complex number. Thus, the conjugate of (a+bi) is (a-bi). The conjugate of (2-3i) is (2+3i). Whenever you multiply by a fraction whose numerator and denominator are identical, the value is just 1. This is a useful tool for simplifying complex numbers, particularly for division problems. Thus, set up the example (4+3i)(2−2i){\displaystyle {\frac {(4+3i)}{(2-2i)}}} as follows:  (4+3i)(2−2i)∗(2+2i)(2+2i){\displaystyle {\frac {(4+3i)}{(2-2i)}}*{\frac {(2+2i)}{(2+2i)}}} Then multiply the numerator and denominator and simplify as follows:  (4+3i)(2−2i)∗(2+2i)(2+2i){\displaystyle {\frac {(4+3i)}{(2-2i)}}*{\frac {(2+2i)}{(2+2i)}}} 8+8i+6i+6i24+4i−4i−4i2{\displaystyle {\frac {8+8i+6i+6i^{2}}{4+4i-4i-4i^{2}}}} 8+14i+6(−1)4−4(−1){\displaystyle {\frac {8+14i+6(-1)}{4-4(-1)}}} 8+14i−64+4{\displaystyle {\frac {8+14i-6}{4+4}}} 2+14i8{\displaystyle {\frac {2+14i}{8}}}   Notice in the second step above, the denominator contains the terms +4i{\displaystyle +4i} and −4i{\displaystyle -4i}. These will cancel each other out. This will always happen as a result of multiplying by the conjugate. The imaginary terms of the denominator should always cancel and disappear. Recognize that the single denominator applies equally to both portions of the numerator. Split the numerator apart to create a standard complex number. 2+14i8=28+14i8=14+7i4{\displaystyle {\frac {2+14i}{8}}={\frac {2}{8}}+{\frac {14i}{8}}={\frac {1}{4}}+{\frac {7i}{4}}}
Question: What is a summary of what this article is about?
Write the division of two complex numbers as a fraction. Find the conjugate of the denominator. Multiply the numerator and denominator by the conjugate of the denominator. Return to complex number format.
Article: . If you haven't already done so, create a plan for what to do in the event of a recession. This risk management plan should include a set of actions you plan to take in the event that you lose business or customers due to an economic downturn. After all, it will be easier to think of what to do before a recession that in the heat of the moment as your employees are panicking and unsure of what to do. Make sure to create concrete steps to follow and then transmit the plan to other managers or partners so that they can follow it as well. Your first course of action when hit by a recession should be to cut expenses where you can. This will help your business stay in operation while you work out a more permanent solution or until the economy recovers. Look around to reduce overhead costs like utilities, administration, and wasted materials. You can also reduce your inventory levels so that your assets aren't so tied up in product that may go unsold for months. If those don't work, consider:  Cutting your advertising spending. Pull out of traditional advertising like television and radio and instead focus on improving your social media presence. Doing so is free, even though it might take more of your time. Downsizing. Your other option to downsize. This can mean either reducing employees or moving to a cheaper location. Your remaining employees may have to work harder, but your business will at least be able to survive. If you do end up letting some employees go, you will need others to step into their roles. This is why it is important to cross-train your employees for various roles within the business. This is best if done before it is needed. You should focus all of your efforts on retaining regular customers and maintaining your relationships with them. Make sure that they know that their business is appreciated. In addition, keep your quality just as high as before, even it you've had to make other cuts around the business. A recession is also a good opportunity to evaluate your customers. You may have those customers who are not profitable to work with. A recession is the perfect time to sever these relationships and seek new ones. Many businesses turn to deals and sales when the recession is hurting them. However, doing so will only make it harder for customers to justify paying your regular prices when the recession is over. In addition, these lower prices can cut into much needed profits. The only exception is that you may want to offer one-time payment extensions or discounts to customers that are also having a hard time. Just be clear to them that you are only extending this service once.
Question: What is a summary of what this article is about?
Develop a risk management plan Reduce expenses. Cross-train your employees. Focus on customers. Don't cut your prices.