Answer:
[tex]\displaystyle \boxed{±3i + 4 = p}[/tex]
Step-by-step explanation:
(p - 2)² = −9
p² - 4p + 4 = −9
+ 9 + 9
____________
p² - 4p + 13
Since this equation is unfactorable with rational numbers, apply the Quadratic Formula:
[tex]\displaystyle -b ± \frac{\sqrt{b^2 - 4ac}}{2a} = p[/tex]
[tex]\displaystyle 4 ± \frac{\sqrt{4^2 - 4[1][13]}}{2[1]} = p[/tex]
[tex]\displaystyle 4 ± \frac{\sqrt{16 - 52}}{2} = p[/tex]
[tex]\displaystyle 4 ± \frac{\sqrt{-36}}{2} = p[/tex]
[tex]\displaystyle 4 ± \frac{6i}{2} = p[/tex]
[tex]\displaystyle 4 ± 3i = p[/tex]
** The above answer is written in reverse, which is the exact same result.
I am joyous to assist you anytime.
