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

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

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

expand

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

z^{2} - 2 z + 1

Solution steps

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

Apply FOIL method:

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

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

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

Apply minus-plus rules

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

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

Simplify

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

= z^{2} - 2 z + 1

k + (2 (l - k) + 1)^{\frac{1}{2}} - 1

5.5 (2.5 t - 6.25 + 6.25 e^{- 0.4 t})

\frac{( 2 x + 3 ) ( 3 x + 4 )}{6}

(1 + 3) i

- \frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

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