vereinfachen-i(x+iy)^2

Lösung

vereinfachen

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

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

Schritte zur Lösung

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

Schreibe

(x + i y)^{2}

um:

x^{2} + 2 x y i - y^{2}

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

Wende das Distributivgesetz an:

m (a + b + c) = ma + mb + m c

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

= - i x^{2} - i 2 x y i - i (- y^{2})

- i x^{2} = - x^{2} i

- i 2 x y i = 2 x y

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

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

Rewrite in standard complex form:

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

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

e x p an d - \frac{2}{( x - 1 ) ^{2} ( x + 1 ) ^{2}}

e x p an d (- y^{3} + y) d y

e x p an d (t^{2} e^{- t} - 4 t e^{- t} + 2 e^{- t})^{2}

e x p an d \frac{1}{( a - b ) ^{2}}

e x p an d (e^{15 x} - 3 x^{2} y) d y