What is expand (3+2i)^2 ?

The solution to expand (3+2i)^2 is 5+12i

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expand (3+2i)^2

expand

(3 + 2 i)^{2}

5 + 12 i

Solution steps

(3 + 2 i)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

3^{2} + 2 \cdot 3 \cdot 2 i + (2 i)^{2} : 12 i + 5

= 12 i + 5

Rewrite in standard complex form:

5 + 12 i

= 5 + 12 i

\frac{sin ( 2 x ) ( cot ( x ) - csc ( x ) )}{cot ( x ) + csc ( x )}

\frac{2 x ^{5} - x ^{4} + 3 x ^{3} - a x ^{2} + b x - c}{( x - 1 ) ^{3}}

5000 (- 0.125 e^{- 0.125 x} x + 1.75 e^{- 0.125 x})

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

(α_{0} + α_{1} t + α_{2} t^{2})^{2} e^{t^{2}}