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2 years ago

The conjugate of (2+i)²/3+i, in the form of a+ib, is

Mathematics

1 answer:

goblinko [34]2 years ago

5 0

Given that

(2+i)²/(3+i)

On multiplying both numerator and the denominator with (3-i) then

⇛ [(2+i)²/(3+i)]×[(3-i)/(3-i)]

⇛ [(2+i)²(3-i)]/[(3+i)(3-i)]

⇛ [(2+i)²(3-i)]/[(3²-i²)

⇛ [(2+i)²(3-i)]/(9-i²)

⇛ [(2+i)²(3-i)]/[9-(-1)]

Since ,i² = -1

⇛ [(2+i)²(3-i)]/(9+1)

⇛ [(2+i)²(3-i)]/10

⇛ [{2²+i²+2(2)(i)}(3-i)]/10

⇛ (4+i²+4i)(3-i)/10

⇛ (4-1+4i)(3-i)/10

⇛ (3+4i)(3-i)/10

⇛ (9-3i+12i-4i²)/10

⇛ (9+9i-4(-1))/10

Since, i² = -1

⇛(9+9i+4)/10

⇛(13+9i)/10

⇛ (13/10)+ i (9/10)

We know that

The conjugate of a+ib is a-ib

So,

The conjugate of (13/10)+ i (9/10) is

(13/10)-i(9/10) ⇛ (13/10)+i (-9/10)

Answer:-The conjugate of (13/10)+ i (9/10) is (13/10)+i (-9/10)

Additional comment:

The conjugate of a+ib is a-ib and
i = -1
(a+b)² = a²+2ab+b² • (a+b)(a-b)=a²-b² •(a-b)²=a²-2ab+b².

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Step-by-step explanation:

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Those who liked the proposed plan=380 persons

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Step-by-step explanation:

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Answer:

Step-by-step explanation:

To find the area of the shaded region, you have to start off with the area of the whole triangle. To find that, you multiply the height and length. length=10 height=8 (10x8=80). Then, since it's a triangle, you have to divide it by two (80/2=40). So, 40 is the area of the whole triangle. Then, you find the area of the white region, which is 12 (3x4=12). Finally, you take the area of the white square and subtract it from the area of the whole triangle (80-12=28). You would get 28.

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Answer:

The height of the triangle could be found by the Pythagoras theorem, where the result is, with the data of the exercise:

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And the area of the triangle is:

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Step-by-step explanation:

When you have two measurements of a triangle, as the case in the picture, you can find the third with the Pythagoras theorem, which is:

(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2

As you can see in the picture, the measurement of the hypotenuse is 12, and the opposite leg could be 6, for this reason, we're gonna clear the adjacent leg of the formula above:

(opposite leg)^2 + (adjacent leg)^2 = hypotenuse^2
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Now, we can replace the values in the formula obtained:

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Now, as we just need the adjacent leg, we take the square root of both sides:

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