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# Trigonometry: Product and Quotient Theorems

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Hello! I've been having some trouble with one of the questions from my online Trig class. They gave me an example, but when I try to duplicate the process, I am getting messed up somewhere and am missing the question entirely.

I have attached a picture of the question. Any help you can provide me is very greatly appreicated. I've been working on similar questions to this for a long time tonight and it seems that it simply isn't sticking.

Thank you for your help in advance. You guys do amazing things and I find it comforting to know that kind humans such as you exist and help make the world a better place, one math problem at a time! I really appreciate everything you do.

Nov 27, 2018

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$$\text{first thing to do is get it in a nicer form}\\ Z = \dfrac{1}{\dfrac{1}{Z_1}+\dfrac{1}{Z_2}} = \dfrac{Z_1 Z_2}{Z_1+Z_2} ==\\ \dfrac{(30+65i)(70+10i)}{(30+65i)+(70+10i)} = \\ \dfrac{(2100-650)+(4550+300)i}{100+75i} = \\ \dfrac{1450+4850i}{100+75i} = \\ \dfrac{58+194i}{4+3i}$$

$$\text{Now to finish it off we should rewrite it so the denominator is real}\\ \dfrac{58+194i}{4+3i} = \dfrac{58+194i}{4+3i} \cdot \dfrac{4-3i}{4-3i} = \\ \dfrac{814+602i}{25}= 32.56 + 24.08i ~\Omega$$

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Nov 27, 2018
edited by Rom  Nov 27, 2018
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I see. Thank you so much for your help. I think it makes more sense now! I really appreicate it!

However, I think the answer is supposed to be in terms of a+bi. Would you be able to help me transform it in the described form?