simplify (4y-3i)^2

Solution

simplify

(4 y - 3 i)^{2}

(16 y^{2} - 9) - 24 y i

Solution steps

(4 y - 3 i)^{2}

Apply Perfect Square Formula:

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

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

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

(4 y)^{2} = 16 y^{2}

- 2 \cdot 4 y \cdot 3 i = - 24 y i

(3 i)^{2} = - 9

= 16 y^{2} - 24 y i - 9

Rewrite in standard complex form:

(16 y^{2} - 9) - 24 y i

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

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

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

(x - 2 - 3) (x - 2 + 3)

(a - x)^{2}

(sec (θ) - tan (θ)) (csc (θ) + 1)