Question

Let A(w^2), B(2iw) and C(-4) be three points lying on the plane.
Now a point P is taken on the circumcircle of the triangle ABC such that
PA. BC = PC AB, (where P, A, B, C are in order). If z is the complex number associated with the mid – point of PB, then the value of 212 is, (w is a
non real cube root of unity)
​

Answer 1

Answer:

A coin is tossed a single time, Find the following probabilities2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??6y=12 solve the equation if 2 X + 3 is equal to zero then what is the value of xA coin is tossed a single time, Find the following probabilities2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??if 2 X + 3 is equal to zero then what is the value of xA coin is tossed a single time, Find the following probabilities2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??

Step-by-step explanation:

A coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilities

A coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesif 2 X + 3 is equal to zero then what is the value of x2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??6y=12 solve the equation A coin is tossed a single time, Find the following probabilitiesif 2 X + 3 is equal to zero then what is the value of x2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??2x+3=0

2x=0-3

2x=-3/2

Or

1.5

??6y=12 solve the equation A coin is tossed a single time, Find the following probabilitiesif 2 X + 3 is equal to zero then what is the value of xif 2 X + 3 is equal to zero then what is the value of xif 2 X + 3 is equal to zero then what is the value of xA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilitiesA coin is tossed a single time, Find the following probabilities

Answer 2

Answer:

PA. BC = PC AB, (where P, A, B, C are in order). If z is the complex number associated with the mid – point of PB, then the value of 212 is, (w is a non real cube root of unity$-\frac{\mathbf{z}_2 \mathbf{z}_3}{\mathbf{z}_1}$.

Step-by-step explanation:

Step : 1

$\begin{array}{ll}\left|z_1\right|= & \left|z_2\right|=\left|z_3\right|=|z| \\\Rightarrow & z_1 \bar{z}_1=z_2 \bar{z}_2=z_3 \bar{z}_3=z \bar{z} \\\because & \text { AP } \perp \mathrm{BC}\end{array}$

$\begin{aligned}& \therefore \quad \frac{z-z_1}{\bar{z}-\bar{z}_1}+\frac{z_2-z_3}{\bar{z}_2-\bar{z}_3}=0 \\& \Rightarrow \quad \frac{z-z_1}{\frac{z_1 \bar{z}_1}{z}-\bar{z}_1}+\frac{z_2-z_3}{\frac{z_3 \bar{z}_3}{z_2}-\bar{z}_3}=0\end{aligned}$

$\begin{aligned}& \Rightarrow \quad-\frac{z}{\bar{z}_1}-\frac{z_2}{\bar{z}_3}=0 \\& \Rightarrow \quad z=-\frac{\bar{z}_1 z_2}{\bar{z}_3}=-\frac{z_2 z_3}{z_1}\end{aligned}$

Step : 2 The following are the steps to build the circumcenter: Draw the perpendicular bisector of any two of the triangle's sides in step one. Step 2: Extend the perpendicular bisectors using a ruler until they cross. Step 3: Label P, the intersection point, which will serve as the triangle's circumcenter.

Step : 3 F is the side AB's perpendicular bisector. The circumcenter of triangle ABC is the location where the three perpendicular bisectors converge, as shown in the sketch. The radius of a circle that goes through the three vertices is the common distance since the circumcenter and the three vertices are equally spaced apart. The circumradius of a triangle with sides measuring a, b, and c has the following length: R is equal to (abc) / ((a + b + c)(b + c - a)(c + a - b)(a + b - c)).

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