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Airida [17]
3 years ago
9

Please help simplify and write your answer in the form a + bi

Mathematics
1 answer:
Tcecarenko [31]3 years ago
5 0

Answer:

2 - 4i

Step-by-step explanation:

\frac{10}{1 + 2i}  \\  \\  =  \frac{10}{1 + 2i}  \times  \frac{1  -  2i}{1  -  2i}  \\  \\  =  \frac{10(1 - 2i)}{ {1}^{2} -  {(2i)}^{2}  }  \\  \\   =  \frac{10 - 20i}{ {1} -  {4i}^{2}  }  \\  \\  =  \frac{10 - 20i}{ {1} -  {4( - 1)} }  \\ ( \because \:  {i}^{2} =  - 1)  \\  \\  =  \frac{10 - 20i}{1 + 4} \\  \\  =  \frac{5(2 - 4i)}{5}  \\  \\  = 2 - 4i

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Which expression is equivalent to 16^3?
Sveta_85 [38]

Answer:

2¹²

Step-by-step explanation:

one expression equivalent to 16³ is 2¹²

think about it like this: we know that 2 to the power of 4 is 16

(2 x 2 = 4, x 2 = 8, x 2 = 16)

So for every "16" we already have 2⁴; meaning that 16³ is the same thing as 3 groups of 2⁴ -- which is 2¹²

hope this helps! have a lovely day :)

4 0
2 years ago
How many license plates can be made using 3 digits and 3 letters of repeated digits and letters are allowed? how many can be mad
BARSIC [14]

26 total letters, 10 total digits

with repeated letters/numbers:

26 * 26 *26 * 10* 10*10 = 17,576,000 ways


without repeats:

26 *25*24 *10 *9*8 = 11,232,000 ways

8 0
3 years ago
Multiply. Write your answer as a fraction or as a whole or mixed number.<br> 4/5 x 3 2/3
julsineya [31]

Answer:

1 14/15

Step-by-step explanation:

Change 3 2/3 into an improper fraction, which is 11/3. When multiplying fractions, you can multiply straight across, so 11*4= 44 and 3*5 equals 15. 44/15 as a mixed fraction is 1 14/15

4 0
3 years ago
The distance between two cities on a map is 3.25 centimeters. The map used a scale in which 1 centimeter represents 20 kilometer
____ [38]

Answer:

<h2> 65km</h2>

Step-by-step explanation:

Step one:

given

we are told that the distance is 3.25cm on the map

the scale is 1cm to represent 20km

Required

the actual distance

Step two

if 1cm represent 20km

then 3.25cm will represent x km

cross multiply we have

x=2.35*20

x= 65km

Hence,  the actual distance between these two cities in kilometers  65km

6 0
3 years ago
What is the product ? 2x(x-4)
Colt1911 [192]

Answer:

2x^2- 8x

Step-by-step explanation:

2x(x-4)

distribute; multiply parenthesis by 2 x

2x * x-2x *4

calculate products

2x^2- 8x

5 0
3 years ago
Read 2 more answers
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