simplify i(x+yi)^2

Solution

simplify

i (x + y i)^{2}

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

Solution steps

i (x + y i)^{2}

Expand

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

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

Apply the distributive law:

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

lo g_{4} (10 x)

- 2 (3 (0) - 5 = 10)

(4 + \frac{37044}{x ^{3}}) x^{2}

9 (x sin (θ) + y cos (θ))^{2}

\frac{( 160 p ^{4} - 7 q ^{9} ) ^{3}}{1000}