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vlabodo [156]
3 years ago
13

Devon is saving money for a ski trip. He has already saved $62.50, but his goal is to save at least $100. What is the least amou

nt Devon needs to save to reach his goal? Let m= money:
Mathematics
1 answer:
ss7ja [257]3 years ago
6 0

Answer:

Step-by-step explanation:

You have to divide 100 by 62.50= m answer

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Match each quotient with its answer when expressed in the form of a + bi.
kykrilka [37]

There is a typo in the available options for this problem. BOTH options B and E are 3/25+4/25i. One of those options should be 3/25-4/25i. So check your problem carefully and be sure to select the correct answer.

1. D. 1 + 0i
2. A. -7/25 + 24/25i
3. B or E, 3/25 + 4/25i
4. F. 3-4i
5. B or E, 3/25 - 4/25i
6. C. -7/25 -24/25i

For this problem, you need to perform complex division, then select the matching answer from the available options. In order to perform a complex division, simply multiply the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator is simply the denominator with the sign of the complex term inverted. So:
1. i/i
Let's rewrite as (0 + i)/(0 + i)
(0 + i)/(0+i) * (0 - i)/(0 - i) 
= (0*0 + 0*i - 0*i - i^2)/(0*0 + 0*i - 0*i - i^2)
= (0 - -1)/(0 - -1)
= 1/1
= 1 + 0i which is option "D"

2. 3+4i/3-4i
3+4i/3-4i * 3+4i/3+4i
= (9 + 12i + 12i + 16i^2) / (9 - 12i + 12i - 16i^2)
= (-7 + 24i) / 25
= -7/25 + 24/25i, which matches option "A"

3. 1/3-4i
1/3-4i * 3+4i/3+4i
= (3 + 4i)/(9 + 12i - 12i - 16i^2)
= (3 + 4i)/(9 - -16)
= (3 + 4i)/25

= 3/25 + 4/25i, which matches option "B" or "E". BE SURE TO SELECT THE
CORRECT OPTION. You want 3/24 PLUS 4/25i.

4. 3-4i/1 
3-4i/1 * 1/1 = 3-4i, which matches option "F"

5. 1/3+4i 
1/3+4i * 3-4i/3-4i
= 3-4i/(9 + 12i - 12i - 16i^2)
= 3-4i/25
= 3/25 - 4/25i, which matches option "B" or "E". BE SURE TO SELECT THE
CORRECT OPTION. You want 3/24 MINUS 4/25i.


6. 3-4i/3+4i
3-4i/3+4i * 3-4i/3-4i
= (9 - 12i - 12i + 16i^2) / (9 - 12i + 12i - 16i^2)
= (9 - 12i - 12i + -16) / (9 - 12i + 12i - -16)
= (-7 - 24i) / 25
= -7/25 -24/25i, which matches option "C"
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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