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1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
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Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
Answer:
40 Bran Muffins
80 Blueberry Muffins
Explanation:
Let the number of Bran muffins ordered = x
The number of Blueberry muffins ordered = 2x <em>(it is given that the number of blueberry muffins is twice the number of bran muffins)</em>
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The cost of Bran muffins ordered = Number of Bran muffins * cost of 1 muffin
Cost of Bran muffins ordered = x * 2
Cost of Bran Muffins ordered = $ 2x
The cost of Blueberry muffins ordered = Number of Blueberry muffins * Cost of 1 blueberry muffin
Cost of Blueberry muffins ordered = 2x * 4
Cost of Blueberry muffins ordered = $ 8x
Since the sum of costs of Blueberry and Bran muffins is $400
Cost of Bran muffins + Cost of Blueberry muffins ordered = 400
2x + 8x = 400
10x = 400
x = 40
Hence, the number of Bran muffins ordered is 40
we are told that the number of Blueberry muffins is twice the number of Bran muffins
So,
Blueberry muffins = Bran muffins * 2
Blueberry Muffins = 40 * 2
Blueberry muffins = 80
So, the number of Blueberry muffins is 80
Answer:
c
Explanation:
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