What is the quotient of the complex number 4-3i divided by its conjugate?
1 answer:
Answer: C.
Step-by-step explanation:
1. You have the following division:
(As you can see, to find the conjugate of 4-3i you must change the sign between the terms).
2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:
3. Keeping on mind that , you have:
4. Simplifying:
5. The result is:
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Let
A------> <span>(5√2,2√3)
B------> </span><span>(√2,2√3)
we know that
</span>the abscissa<span> and the ordinate are respectively the first and second coordinate of a point in a coordinate system</span>
the abscissa is the coordinate x<span>
step 1
find the midpoint
ABx------> midpoint AB in the coordinate x
</span>ABy------> midpoint AB in the coordinate y
<span>
ABx=[5</span>√2+√2]/2------> 6√2/2-----> 3√2
ABy=[2√3+2√3]/2------> 4√3/2-----> 2√3
the midpoint AB is (3√2,2√3)
the answer is
the abscissa of the midpoint of the line segment is 3√2
see the attached figure
A------> <span>(5√2,2√3)
B------> </span><span>(√2,2√3)
we know that
</span>the abscissa<span> and the ordinate are respectively the first and second coordinate of a point in a coordinate system</span>
the abscissa is the coordinate x<span>
step 1
find the midpoint
ABx------> midpoint AB in the coordinate x
</span>ABy------> midpoint AB in the coordinate y
<span>
ABx=[5</span>√2+√2]/2------> 6√2/2-----> 3√2
ABy=[2√3+2√3]/2------> 4√3/2-----> 2√3
the midpoint AB is (3√2,2√3)
the answer is
the abscissa of the midpoint of the line segment is 3√2
see the attached figure
For this case we have that by definition, the Greatest Common Factor or GFC of two or more numbers, is the largest number that divides them without leaving residue.
So:
We look for the factors of 18 and 36:
18: 1,2,3,6,9,18
36: 1, 2,3,4, 6,9,18 ...
Thus, the GFC of both numbers is 18.
Then, the GFC of and
is:
Answer:
In a 45 - 45 - 90 right triangle, the hypotenuse is √2 · legs = hypotenuse, so legs= and to rationalize the denominator all we have to do is multiply the numerator and denominator by √2.
.