What is the principal square root of -4

Mathematics

1 answer:

devlian [24]4 years ago

6 0

Answer:

The principal square root of -4 is 2i.

Step-by-step explanation:

$\sqrt{-4}$ = 2i

We have the following steps to get the answer:

Applying radical rule $\sqrt{-a} =\sqrt{-1} \sqrt{a}$

We get $\sqrt{-4} =\sqrt{-1} \sqrt{4}$

As per imaginary rule we know that $\sqrt{-1}=i$

= $\sqrt{4} i$

Now $\sqrt{4} =2$

Hence, the answer is 2i.

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siniylev [52]

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In ΔABC right angled at A, D and E are points on BC, C such that BD = CD and AD ⊥ BC

$\underline{\underline{\large\bf{Solution:-}}}\\$

$\longrightarrow$ Let us know about definition of altitude first. The altitude of a triangle is the perpendicular line segment drawn from the vertex to the opposite side of the triangle.

$\leadsto$ Median is the line segment from a vertex to the midpoint of the opposite side.

Let us Check all options one by one

CD is line segment which starts from vertex C but don't falls on opposite side AB thus it is not an altitude.❌

BA is line segment which starts from vertex B and falls perpendicularly on opposite sides AC and is thus an altitude.✔️

AD is line segment which starts from vertex A and falls perpendicularly on opposite side BC and is thus an altitude.✔️

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8 0

2 years ago

Find, corrrect to the nearest degree, the three angles of the triangle with the given vertices. D(0,1,1), E(-2,4,3), C(1,2,-1)

Sholpan [36]

Answer:

The three angles of the triangle given above are 23, 73 and 84 correct to the nearest degree. The concept of dot product under vectors was applied in solving this problem. The three positions forming the triangle were taken as positions vectors. The Dot product also known as scalar product is a very good way of finding the angle between two vectors. ( in this case the sides of the triangle given above). Below is a picture of the step by step procedure of the solution.

Step-by-step explanation:

The first thing to do is to treat the given positions in space as position vectors which gives us room to perform vector manipulations on them. Next we calculate the magnitude of the position vector which is the square root of the sun of the square of the positions of the vectors along the three respective axes). Then we calculate the dot product. After this is calculated the angle can then be found easily using formula for the dot product.

Thank you for reading this and I hope it is helpful to you.