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In which quadrant is the number [tex]\(6 - 8i\)[/tex] located on the complex plane?

A. I
B. II
C. III
D. IV

Sagot :

GinnyAnsweridn
To determine the quadrant in which the complex number [tex]\( 6 - 8i \)[/tex] is located, we need to analyze its real and imaginary parts.

A complex number is given in the form [tex]\( a + bi \)[/tex], where:
- [tex]\( a \)[/tex] is the real part.
- [tex]\( b \)[/tex] is the imaginary part.

For the number [tex]\( 6 - 8i \)[/tex]:
- The real part ([tex]\( a \)[/tex]) is [tex]\( 6 \)[/tex].
- The imaginary part ([tex]\( b \)[/tex]) is [tex]\( -8 \)[/tex].

Now, we need to determine the quadrant based on these parts:
1. Quadrant I: In this quadrant, both the real part and the imaginary part are positive ([tex]\( a > 0 \)[/tex] and [tex]\( b > 0 \)[/tex]).
2. Quadrant II: In this quadrant, the real part is negative and the imaginary part is positive ([tex]\( a < 0 \)[/tex] and [tex]\( b > 0 \)[/tex]).
3. Quadrant III: In this quadrant, both the real part and the imaginary part are negative ([tex]\( a < 0 \)[/tex] and [tex]\( b < 0 \)[/tex]).
4. Quadrant IV: In this quadrant, the real part is positive and the imaginary part is negative ([tex]\( a > 0 \)[/tex] and [tex]\( b < 0 \)[/tex]).

Since for [tex]\( 6 - 8i \)[/tex]:
- The real part [tex]\( a = 6 \)[/tex] is positive.
- The imaginary part [tex]\( b = -8 \)[/tex] is negative.

Therefore, the complex number [tex]\( 6 - 8i \)[/tex] is located in Quadrant IV.

So, the correct answer is:
IV.
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