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

tan (\frac{x}{2}) + (1 - cos (x)) cot (x)

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

(e^{- x} - e^{- x} x)^{2}

(x + \frac{4}{5}) (x - \frac{3}{5})

x x (3 ln (x) - 2)