What is expand (2pi+i2pin)*(2pi-i*2pin) ?

The solution to expand (2pi+i2pin)*(2pi-i*2pin) is 4pi^2-4pi^2i^2n^2

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expand (2pi+i2pin)(2pi-i2pin)

expand

(2 π + i 2 πn) \cdot (2 π - i \cdot 2 πn)

4 π^{2} - 4 π^{2} i^{2} n^{2}

Solution steps

(2 π + i \cdot 2 πn) (2 π - i \cdot 2 πn)

= (2 π + 2 πin) (2 π - 2 πin)

Apply Difference of Two Squares Formula:

(a + b) (a - b) = a^{2} - b^{2}

a = 2 π, b = i \cdot 2 πn

= (2 π)^{2} - (i \cdot 2 πn)^{2}

Simplify

(2 π)^{2} - (i \cdot 2 πn)^{2} : 4 π^{2} - 4 π^{2} i^{2} n^{2}

= 4 π^{2} - 4 π^{2} i^{2} n^{2}

\frac{L ^{2} ( P + W L )}{16}

\frac{3 ( k ^{2} + 3 k + 2 )}{2}

\frac{( x - 3 ) ( x + 2 )}{( x + 3 )}

\frac{( 2 x ^{2} - 6 x + 9 ) ^{2}}{2}

(35) (67)

What is expand (2pi+i2pin)*(2pi-i*2pin) ?
The solution to expand (2pi+i2pin)*(2pi-i*2pin) is 4pi^2-4pi^2i^2n^2