In which quadrant is the number 6 – 8i located on the complex plane?
2 answers:
Answer:
A complex number Z = A + Bi can be represented in the same way like we represent a point (a,b) in the coordinate plane.
Like in two dimensional coordinate system where there is X axis and Y Axis In complex plane , for locating real part of complex number we use X axis and for locating imaginary part we use Y axis.
So Complex number Z= 6 - 8 i = Point in the complex plane (6,-8)
6 = Real Part = Positive real number
-8 = Imaginary Part = Negative real number
Point (6,-8) will lie in Fourth Quadrant.
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Answer:
The vertex of this parabola, , can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where ,
, and
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for , and the coefficient for
should all match accordingly. That is:
.
The first equation implies that is equal to
. Hence, replace the "
" in the second equation with
to eliminate
:
.
.
Similarly, replace the "" and the "
" in the third equation with
and
, respectively:
.
.
Therefore, would be equivalent to
. The vertex of this parabola would thus be:
.