To determine the real part of the complex number [tex]\( -3 + 9i \)[/tex], we need to examine its structure.
A complex number typically takes the form [tex]\( a + bi \)[/tex], where:
- [tex]\( a \)[/tex] is the real part, and
- [tex]\( bi \)[/tex] is the imaginary part, with [tex]\( b \)[/tex] being the coefficient of the imaginary unit [tex]\( i \)[/tex].
Given the complex number [tex]\( -3 + 9i \)[/tex]:
- The number [tex]\( -3 \)[/tex] is in the position of [tex]\( a \)[/tex],
- The number [tex]\( 9 \)[/tex] is in the position of [tex]\( b \)[/tex], attaching to [tex]\( i \)[/tex].
Thus, the real part of the complex number [tex]\( -3 + 9i \)[/tex] is [tex]\( -3 \)[/tex].
Therefore, the correct answer is:
c. [tex]\(-3\)[/tex].
