simplify (x+9i)^2

Solution

simplify

(x + 9 i)^{2}

(x^{2} - 81) + 18 x i

Solution steps

(x + 9 i)^{2}

Apply Perfect Square Formula:

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

(x + 9 i)^{2} = x^{2} + 2 x \cdot 9 i + (9 i)^{2}

= x^{2} + 2 x \cdot 9 i + (9 i)^{2}

2 x \cdot 9 i = 18 x i

(9 i)^{2} = - 81

= x^{2} + 18 x i - 81

Rewrite in standard complex form:

(x^{2} - 81) + 18 x i

= (x^{2} - 81) + 18 x i

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