What is expand (z-e^{pi/4})(z-e^{-pi/4}) ?

The solution to expand (z-e^{pi/4})(z-e^{-pi/4}) is -z/(e^{pi/4)}+z^2-e^{pi/4}z+1

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expand (z-e^{pi/4})(z-e^{-pi/4})

expand

(z - e^{\frac{π}{4}}) (z - e^{- \frac{π}{4}})

- \frac{z}{e ^{\frac{π}{4}}} + z^{2} - e^{\frac{π}{4}} z + 1

Solution steps

(z - e^{\frac{π}{4}}) (z - e^{- \frac{π}{4}})

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = z, b = - e^{\frac{π}{4}}, c = z, d = - e^{- \frac{π}{4}}

= zz + z (- e^{- \frac{π}{4}}) + (- e^{\frac{π}{4}}) z + (- e^{\frac{π}{4}}) (- e^{- \frac{π}{4}})

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= zz - e^{- \frac{π}{4}} z - e^{\frac{π}{4}} z + e^{- \frac{π}{4}} e^{\frac{π}{4}}

Simplify

zz - e^{- \frac{π}{4}} z - e^{\frac{π}{4}} z + e^{- \frac{π}{4}} e^{\frac{π}{4}} : - \frac{z}{e ^{\frac{π}{4}}} + z^{2} - e^{\frac{π}{4}} z + 1

= - \frac{z}{e ^{\frac{π}{4}}} + z^{2} - e^{\frac{π}{4}} z + 1

- \frac{7 x + 15}{( x - 1 ) ^{2}}

A (A + B^{^{'}} C) + A (B^{^{'}} + C)

(2 e^{x} - 1)^{2}

(n + 1)^{2}!

5 x^{2} + x^{2}

What is expand (z-e^{pi/4})(z-e^{-pi/4}) ?
The solution to expand (z-e^{pi/4})(z-e^{-pi/4}) is -z/(e^{pi/4)}+z^2-e^{pi/4}z+1