INPUT ARTICLE: Article: Looking at a complex number (a+bi) should remind you of binomials from Algebra or Algebra 2. Remember that to multiply binomials, you need to multiply each term of the first binomial by each term of the second. A shorthand version for doing this, is the F-O-I-L rule, which stands for "First, Outer, Inner, Last." For an example of (a+b)(c+d), apply this rule as follows: First. The F in FOIL means that you multiply the first term of the first binomial by the first term of the second binomial. For the sample, this would be a*c. Outer. The O in FOIL tells you to multiply the "outer" terms. These are the first term of the first binomial and the second term of the second binomial. For the sample, this would be a*d. Inner. The I in FOIL means to multiply the "inner" terms. These would be the two terms that appear in the middle, which are the second term of the first binomial and the first term of the second binomial. In the given example, the inner terms are b*c. Last. The L in FOIL represents the last terms of each binomial. For the sample expression, this would be b*d. Finally, add all four products together. The result for the sample binomial multiplication of (a+b)(c+d) is ac+ad+bc+bd. To multiply two complex numbers, set them up as the product of two binomials and apply the FOIL rule. For example, the product of the two complex numbers (3+2i)*(5-3i) works as follows: First. The product of the first terms is 3*5=15. Outer. The product of the outer terms is 3*(-3i). This product is -9i. Inner. The product of the two inner terms is 2i*5. This product is 10i. Last. The product of the last terms is (2i)*(-3i). This product is -6i2. Recognize that i2 equals -1, so the value of -6i2 is -6*-1, which is 6. After applying the FOIL rule and finding the four independent products, combine them together to find the result of the multiplication. For the sample (3+2i)*(5-3i), the parts combine to give 15-9i+10i+6. The result of the FOIL rule multiplication should yield two real number terms and two imaginary number terms. Simplify the result by combining like terms together. For the sample 15-9i+10i+6, you can add the 15 and 6 together and add the -9i and the 10i together. The result will be 21+i. Find the product of the two complex numbers (3+4i)(-2-5i). The steps for this multiplication are: (3)(-2)=-6 (First) (3)(-5i)=-15i (Outer) (4i)(-2)=-8i (Inner) (4i)(-5i)=-20i2=(-20)(-1)=20 (Lasts) -6-15i-8i+20 = 14-23i (Combine terms and simplify)

SUMMARY: Remember the F-O-I-L rule. Apply the FOIL rule to complex number multiplication. Combine the terms. Simplify by combining like terms. Work through one more example.

INPUT ARTICLE: Article: Agar usually comes in three forms: powder, flakes, or a bar. All three work equally well; the real difference is ease of preparation. Powdered Agar is usually the easiest to use, as it can be substituted for gelatin in a 1:1 ratio (1 teaspoon gelatin is equivalent to 1 teaspoon Agar powder). The powder also dissolves easier than flakes or bars.If you're not sure which type to use, default to the powdered Agar. Agar bars are white, lightweight and made of freeze-dried Agar. They can be ground in a coffee or spice grinder so they dissolve easier or can be broken up by hand. One bar is equivalent to 2 teaspoons of Agar powder. Agar flakes can also be ground in a coffee or spice grinder and are less concentrated than the powder. They are white and look a little like fish food. 2 tablespoons (29.6ml) of Agar is roughly equivalent to 2 teaspoons of Agar powder. Look for Agar in natural food stores, Asian grocery stores, or online. The firmness of the gel is determined by the amount of Agar you add. If your recipe doesn't give you a measurement, you can follow this rule of thumb: to thicken 1 cup (.25 liters) of liquid, use 1 teaspoon Agar powder, 1 tablespoon (14.8ml) Agar flakes, or 1/2 Agar bar. If you are substituting gelatin with Agar you can use the same amount of Agar powder to thicken the recipe. Otherwise, for every teaspoon of gelatin you will need to use 1 tablespoon (14.8ml) flakes or 1/2 bar. If you are trying to jellify a somewhat acidic liquid, such as those derived from citrus fruits or strawberry, you may need to add more Agar. Some fruits are too acidic or contain enzymes that prevent gelling and must be broken down by being cooked first. These fruits include kiwi, pineapple, fresh figs, papaya, mango, and peaches. Using canned versions of these fruits will cut out the extra step of cooking them, since canned fruits have all been pre-cooked. You can also hydrate the Agar in boiling water and then mix in the acidic liquid. The powder should simmer for about 5 minutes while the flakes and bars should take between 10-15 minutes. Stir the solution until the Agar is completely dissolved. This process will hydrate the Agar, which will allow it to jellify the liquid when it cools. Warm up the liquid as much as possible. One advantage of Agar is that it begins to set at a higher temperature than gelatin, so it is a solid at room temperature or even when you warm it up. The liquid will begin to gel when it falls below 113F (45C). Because the addition of other ingredients may cause the temperature to drop and the Agar to set before you are ready, getting the liquid as hot as you can will make it less likely to drop below 113F (45C) until you remove it from heat. If you are making an alcoholic gel, boil the Agar with any juices or mixers first, then whisk the alcohol in at the very last moment. This will prevent the alcohol from evaporating. The mixture will begin to gel when it reaches 104F to 113F (40C to 45C) and will stay in this form as long as it stays below 175F (80C). You don't need to refrigerate the gel unless you want to serve it cool, so you can leave your dish sitting out at room-temperature without it melting or collapsing. If you're not sure if you used the right amount of Agar, pour a small amount in a cold bowl to see if it firms up. If it doesn't set after 30 seconds, add more Agar. If it's too firm for your liking, add more liquid. Don't stir or shake the Agar jelly until it has completely set, or it will collapse. Don't grease, line, or oil the mold before pouring in the mixture. It should pop out of your mold just fine, and these things can actually affect how well your mixture gels. Unlike gelatin, you can melt the gelled mixture (if you wanted to add another ingredient, pour it into a different mold, add more agar to make the gel more firm or add more liquid to soften it), bring it to a boil again, then cool it again without compromising its gelling abilities.

SUMMARY:
Find Agar and decide which form works best for you. Add Agar to the liquid and mix with a whisk. Bring the solution to a boil and allow it to simmer. Pour the mixture into a mold or container and leave it out at room-temperature to gel.