simplify (3x+4i)^2

Solution

simplify

(3 x + 4 i)^{2}

(9 x^{2} - 16) + 24 x i

Solution steps

(3 x + 4 i)^{2}

Apply Perfect Square Formula:

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

(3 x + 4 i)^{2} = (3 x)^{2} + 2 \cdot 3 x \cdot 4 i + (4 i)^{2}

= (3 x)^{2} + 2 \cdot 3 x \cdot 4 i + (4 i)^{2}

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

2 \cdot 3 x \cdot 4 i = 24 x i

(4 i)^{2} = - 16

= 9 x^{2} + 24 x i - 16

Rewrite in standard complex form:

(9 x^{2} - 16) + 24 x i

= (9 x^{2} - 16) + 24 x i

- 2 (2 + 2 - 2)

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

(z + 2 i)^{2}

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

(cos^{2} (x) + sec^{2} (x)) (cos^{2} (x) - 2)