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Points on a Cartesian Plane

In the x-y co...

Question

In the x-y coordinate system point (-3, -3) lies in which quadrant?

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Solution

The terminal arm passes through $(- 3, - 3)$ .

The point is of the form, $(x, y)$ . Here, $x$ is negative and $y$ is negative, which lies in III quadrant.

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Q. The complex number

z

in the second quadrant which satisfies the equation

z^{3} = 8 i

z

is such that it is equidistance from three distinct points

z_{1}, z_{2}, z_{3}

in Gaussian plane If

z, z_{1}, z_{2}

are collinear, then Arg

(\frac{z_{3} - z_{1}}{z_{3} - z_{2}})

z_{1}, z_{2}, z_{3}

are in anticlockwise sense.

| z_{1} | = | z_{2} | = | z_{3} | = | z_{4} |

z_{1} + z_{2} + z_{3} + z_{4} = 0

then the points

z_{1}, z_{2}, z_{3}, z_{4}

in the Argand plane are the vertices of a

z_{1}, z_{2}, z_{3}, z_{4}

are four points in the Argand plane. If

z

is a point such that

| z - z_{1} | = | z - z_{2} | = | z - z_{3} | = | z - z_{4} |

, then the points

z_{1}, z_{2}, z_{3}, z_{4}

can lie on which among the following curves?

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