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matrenka [14]
2 years ago
6

What is the answer for 4i over 3+7i

Mathematics
1 answer:
icang [17]2 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

given \frac{4i}{3+7i}

To rationalise multiply the numerator/denominator by the conjugate of the denominator

the conjugate of 3 + 7i is 3 - 7i, hence

\frac{4i(3-7i)}{(3+7i)(3-7i)}

distribute the numerator/denominator

= \frac{12i-28i^2}{9-49i^2}

[ note that i² = - 1 ]

= \frac{12i+28}{9+49}

= \frac{28+12i}{58}

= \frac{28}{58} + \frac{12}{58} i

= \frac{14}{29} + \frac{6}{29} i ← in standard form



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Drag the tiles to the correct boxes to complete the pairs.
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Answer:

√8 ==> 2 units, 2 units

√7 ==> √5 units, √2 units

√5 ==> 1 unit, 2 units

3 ==> >2 units, √5 units

Step-by-step explanation:

To determine which pair of legs that matches a hypotenuse length to create a right triangle, recall the Pythagorean theorem, which holds that, for a right angle triangle, the square of the hypotenuse (c²) = the sum of the square of each leg length (a² + b²)

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c² = (√5)² + (√2)²

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The hypothenuse length that matches √5 units, √2 units is √7

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c² = (√3)² + (4)²

c² = 3 + 16 = 19

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This given pair of legs doesn't match any given hypotenuse length

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c² = (2)² + (√5)²

c² = 4 + 5 = 9

c = √9 = 3

legs 2 units, and √5 units matche hypotenuse length of 3

=>2 units, 2 units

c² = 2² + 2² = 4 + 4

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c = √8

Legs 2 units, and 2 units matche hypotenuse length of √8

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c² = 1² + 2² = 1 + 4

c² = 5

c = √5

Leg lengths, 1 unit and 2 units match the hypotenuse length, √5

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