What is expand (2*pi+i*w)^2 ?

The solution to expand (2*pi+i*w)^2 is (4pi^2-w^2)+4piiw

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expand (2pi+iw)^2

expand

(2 \cdot π + i \cdot w)^{2}

(4 π^{2} - w^{2}) + 4 πi w

Solution steps

(2 π + i w)^{2}

Apply Perfect Square Formula:

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

a = 2 π, b = i w

= (2 π)^{2} + 2 \cdot 2 πi w + (i w)^{2}

Simplify

(2 π)^{2} + 2 \cdot 2 πi w + (i w)^{2} : 4 π^{2} + 4 πi w - w^{2}

= 4 π^{2} + 4 πi w - w^{2}

Rewrite

4 π^{2} + 4 πi w - w^{2}

in standard complex form:

(4 π^{2} - w^{2}) + 4 π w i

= (4 π^{2} - w^{2}) + 4 π w i

\frac{s - 1}{s ^{2} ( s ^{3} + 3 s - 1 )}

(x + 2) (x - 2)

x (x - 5)

\frac{( k ^{2} ( k + 1 ) ^{2} )}{4}

- \frac{ln ( 6 )}{3 ( - e ^{\frac{l n ( 6 )}{15}} + 1 )}

What is expand (2*pi+i*w)^2 ?
The solution to expand (2*pi+i*w)^2 is (4pi^2-w^2)+4piiw