simplify (x+2i)^2

Solution

simplify

(x + 2 i)^{2}

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

Solution steps

(x + 2 i)^{2}

Apply Perfect Square Formula:

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

(x + 2 i)^{2} = x^{2} + 2 x \cdot 2 i + (2 i)^{2}

= x^{2} + 2 x \cdot 2 i + (2 i)^{2}

2 x \cdot 2 i = 4 x i

(2 i)^{2} = - 4

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

Rewrite in standard complex form:

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

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

\frac{1}{x ^{3}} (\frac{1}{3 x ^{2}} - \frac{x}{2})^{9}

cos (θ) (csc (θ) - sec (θ))

\frac{180 ( n - 2 )}{n}

(y^{2} - 3 y - x) d x + (2 y - 3) d y

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