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SpyIntel [72]
3 years ago
5

Simplify the expression: (3 − 4i) + (7 − 6i). 4 − 2i 4 − 10i 13 − 2i 10 − 10i

Mathematics
1 answer:
yulyashka [42]3 years ago
7 0

Equivalent expressions are expressions of equal values

The simplified expression of (3 - 4i) + (7 - 6i) is 10- 10i

The expression is given as:

(3 - 4i) + (7 - 6i)

Remove brackets in the above expression

3 - 4i + 7 - 6i

Rewrite the expression by collecting the like terms

3 + 7- 4i  - 6i

Next, evaluate the like terms

10- 10i

Hence, the simplified expression of (3 - 4i) + (7 - 6i) is 10- 10i

Read more about equivalent expressions at:

brainly.com/question/2972832

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Answer:

The length of the unknown sides of the triangles are as follows:

CD = 10√2

AC = 10√2

BC =  10

AB = 10

ΔACD is a right angle triangle. Therefore, Pythagoras theorem can be used to find the sides of the triangle.

c² = a² + b²

where

c = hypotenuse side = AD = 20

a and b are the other 2 legs

lets use trigonometric ratio to find CD,

cos 45 = adjacent / hypotenuse

cos 45 = CD / 20

CD = 1 / √2 × 20

CD = 20 / √2 = 20√2 / 2 = 10√2

20² - (10√2)² = AC²

400 - 100(2)  = AC²

AC² = 200

AC = √200 = 10√2

ΔABC is a right angle triangle too. Therefore,

AB² + BC² = AC²

Using trigonometric ratio,

cos 45 = BC / 10√2

BC = 10√2 × cos 45

BC = 10√2 × 1 / √2

BC = 10√2 / √2 =  10

(10√2)² - 10² = AB²

200 - 100 = AB²

AB² = 100

AB = 10

Step-by-step explanation:

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Answer:

53 1/3 miles.

Step-by-step explanation:

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