+9481 5. \(\frac{-6+i}{-5+i}\)
Multiply the numerator and denominator by -5 - i .
\(=\frac{(-6+i)(-5-i)}{(-5+i)(-5-i)}=\frac{30+6i-5i-i^2}{25+5i-5i-i^2}=\frac{30+i-i^2}{25-i^2}\)
Replace the i2 's with -1 since i2 = -1
\(=\frac{30+i-(-1)}{25-(-1)} =\frac{30+i+1}{25+1} =\frac{31+i}{26}\)
6. \(\frac12x^2-x+5=0\)
We can use the quadratic formula to solve this for x, with a = 1/2 , b = -1 , and c = 5 .
\(x = {-(-1) \pm \sqrt{(-1)^2-4(\frac12)(5)} \over 2(\frac12)} \\~\\ x = {1 \pm \sqrt{1-10} \over 1} \\~\\ x=1\pm\sqrt{-9} \\~\\ x=1\pm i\sqrt9\)
+9481 5. \(\frac{-6+i}{-5+i}\)
Multiply the numerator and denominator by -5 - i .
\(=\frac{(-6+i)(-5-i)}{(-5+i)(-5-i)}=\frac{30+6i-5i-i^2}{25+5i-5i-i^2}=\frac{30+i-i^2}{25-i^2}\)
Replace the i2 's with -1 since i2 = -1
\(=\frac{30+i-(-1)}{25-(-1)} =\frac{30+i+1}{25+1} =\frac{31+i}{26}\)
6. \(\frac12x^2-x+5=0\)
We can use the quadratic formula to solve this for x, with a = 1/2 , b = -1 , and c = 5 .
\(x = {-(-1) \pm \sqrt{(-1)^2-4(\frac12)(5)} \over 2(\frac12)} \\~\\ x = {1 \pm \sqrt{1-10} \over 1} \\~\\ x=1\pm\sqrt{-9} \\~\\ x=1\pm i\sqrt9\)
