simplify (3y-5i)^2

Solution

simplify

(3 y - 5 i)^{2}

(9 y^{2} - 25) - 30 y i

Solution steps

(3 y - 5 i)^{2}

Apply Perfect Square Formula:

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

(3 y - 5 i)^{2} = (3 y)^{2} - 2 \cdot 3 y \cdot 5 i + (5 i)^{2}

= (3 y)^{2} - 2 \cdot 3 y \cdot 5 i + (5 i)^{2}

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

- 2 \cdot 3 y \cdot 5 i = - 30 y i

(5 i)^{2} = - 25

= 9 y^{2} - 30 y i - 25

Rewrite in standard complex form:

(9 y^{2} - 25) - 30 y i

= (9 y^{2} - 25) - 30 y i

(x - 4) (x + 4)

(x - 4) (x + 5) (x - 5)

(5 x - 2)^{2}

(1 + cos (3 t))^{2}

cos (0)