vereinfachen (3x+3iy)^2

Lösung

vereinfachen

(3 x + 3 i y)^{2}

(9 x^{2} - 9 y^{2}) + 18 x y i

Schritte zur Lösung

(3 x + 3 i y)^{2}

Wende Formel für perfekte quadratische Gleichungen an:

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

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

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

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

2 \cdot 3 x \cdot 3 i y = 18 x y i

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

= 9 x^{2} + 18 x y i - 9 y^{2}

Rewrite in standard complex form:

(9 x^{2} - 9 y^{2}) + 18 x y i

= (9 x^{2} - 9 y^{2}) + 18 x y i

e x p an d lo g_{3} (\frac{x}{y ^{3} z ^{2}})

s im pl i f y \frac{( 4 + 3 x ) ^{2}}{x}

e x p an d \frac{3 ( 2 - x ) ^{2}}{2}

e x p an d (2 + 7) 3

e x p an d \frac{( a + 1 ) ^{2}}{( a + 3 ) ( a + 5 )}