Given
[tex]x=\frac{4\pm\sqrt[]{-25}}{4}[/tex]The expression includes the square root of -25. To solve this expression further, you have to use complex numbers.
The unit imaginary number is represented by the letter "i", which is equal to the square root of -1
[tex]i=\sqrt[]{-1}[/tex]You can write the square root of -25 using imaginary numbers as follows:
[tex]\sqrt[]{-25}=\sqrt[]{(-1)\cdot25}=\sqrt[]{-1}\cdot\sqrt[]{25}=i\cdot\sqrt[]{25}[/tex]The square root of 25 is 5 so you can simplify the expression one step more:
[tex]i\sqrt[]{25}=5i[/tex]Now you can write the quadratic equation as follows:
[tex]x=\frac{4\pm5i}{4}[/tex]Distribute the division and simplify:
[tex]\begin{gathered} x=\frac{4}{4}\pm\frac{5i}{4} \\ x=1\pm\frac{5}{4}i \end{gathered}[/tex]"a" represents the real number, in this case, it is a=1
"b" represents the imaginary part of the number, in this case, b=±5/4
The correct option is the first option.