simplify (x+5i)^2

Solution

simplify

(x + 5 i)^{2}

(x^{2} - 25) + 10 x i

Solution steps

(x + 5 i)^{2}

Apply Perfect Square Formula:

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

(x + 5 i)^{2} = x^{2} + 2 x \cdot 5 i + (5 i)^{2}

= x^{2} + 2 x \cdot 5 i + (5 i)^{2}

2 x \cdot 5 i = 10 x i

(5 i)^{2} = - 25

= x^{2} + 10 x i - 25

Rewrite in standard complex form:

(x^{2} - 25) + 10 x i

= (x^{2} - 25) + 10 x i

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