What is (x+i(-x+2))^2 ?

The solution to (x+i(-x+2))^2 is (4x-4)+(-2x^2+4x)i

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simplify (x+i(-x+2))^2

simplify

(x + i (- x + 2))^{2}

(4 x - 4) + (- 2 x^{2} + 4 x) i

Solution steps

(x + i (- x + 2))^{2}

Apply Perfect Square Formula:

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

(x + i (- x + 2))^{2} = x^{2} + 2 x i (- x + 2) + (i (- x + 2))^{2}

= x^{2} + 2 x i (- x + 2) + (i (- x + 2))^{2}

Simplify

x^{2} + 2 x i (- x + 2) + (i (- x + 2))^{2} : 2 x i (- x + 2) + 4 x - 4

= 2 x i (- x + 2) + 4 x - 4

Expand

2 x i (- x + 2) : - 2 x^{2} i + 4 x i

= - 2 x^{2} i + 4 x i + 4 x - 4

Rewrite in standard complex form:

(4 x - 4) + (- 2 x^{2} + 4 x) i

= (4 x - 4) + (- 2 x^{2} + 4 x) i

2 (- 1)^{2} + 2 (- 1)

(14 + tan (x)) (14 - tan (x)) + sec^{2} (x)

\frac{a s}{( a ^{2} - s ^{2} ) ( s ^{2} - a ^{2} )}

(e^{- 7 x} + 9) (e^{- 3 x} + 14)

\frac{0.2 ( 1.5 P + 1.5 T )}{T}