simplify (3x+2i)^2

Solution

simplify

(3 x + 2 i)^{2}

(9 x^{2} - 4) + 12 x i

Solution steps

(3 x + 2 i)^{2}

Apply Perfect Square Formula:

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

(3 x + 2 i)^{2} = (3 x)^{2} + 2 \cdot 3 x \cdot 2 i + (2 i)^{2}

= (3 x)^{2} + 2 \cdot 3 x \cdot 2 i + (2 i)^{2}

(3 x)^{2} = 9 x^{2}

2 \cdot 3 x \cdot 2 i = 12 x i

(2 i)^{2} = - 4

= 9 x^{2} + 12 x i - 4

Rewrite in standard complex form:

(9 x^{2} - 4) + 12 x i

= (9 x^{2} - 4) + 12 x i

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