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Alex787 [66]
2 years ago
10

How many diagonals does a rectangle have?

Mathematics
1 answer:
alexandr402 [8]2 years ago
3 0
A rectangle has 2 diagonals
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The refrigerator part of a refrigerator-freezer has a volume of 27 cubic feet.
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Step-by-step explanation:

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Evaluate (6 + 2i) / (3 –i ).<br> 5/4 + 6/4i<br> 8/5 + 6/5i<br> 20/8 + 12/8i<br> 16/9 + 12/9i
Yuki888 [10]

We are given with a complex no. and need to simplify it , so let's start !!!

Let's assume that :

{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}}

Now , Rationalizing the denominator or in other words multiplying and dividing {z} by the <em>conjugate</em> of the denominator

{:\implies \quad z=\sf \dfrac{6+2\iota}{3-\iota}\times \dfrac{3+\iota}{3+\iota}}

{:\implies \quad z=\sf \dfrac{(6+2\iota)(3+\iota)}{(3-\iota)(3+\iota)}}

{:\implies \quad z=\sf \dfrac{6(3+\iota)+2\iota (3+\iota)}{(3)^{2}-(\iota)^{2}}\quad \qquad \{\because (a-b)(a+b)=a^{2}-b^{2}\}}

{:\implies \quad z=\sf \dfrac{18+6\iota +6\iota +2(\iota)^{2}}{9-(-1)}\quad \qquad \{\because (\iota)^{2}=-1\}}

{:\implies \quad z=\sf \dfrac{18+12\iota -2}{10}}

{:\implies \quad z=\sf \dfrac{16+12\iota}{10}}

{:\implies \quad z=\sf \dfrac{16}{10}+\dfrac{12\iota}{10}}

{:\implies \quad {\bf \therefore}\quad \underline{\underline{z=\bf \dfrac{8}{5}+\dfrac{6}{5}\iota}}}

Hence , Option B) <em>(8/5) + (6/5)i</em> is correct :D

7 0
2 years ago
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