simplify (x+iy)^2-1

Solution

simplify

(x + i y)^{2} - 1

(x^{2} - y^{2} - 1) + 2 x y i

Solution steps

(x + i y)^{2} - 1

Expand

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

= x^{2} + 2 x y i - y^{2} - 1

Rewrite in standard complex form:

(x^{2} - y^{2} - 1) + 2 x y i

= (x^{2} - y^{2} - 1) + 2 x y i

lo g_{9} \frac{9 x ^{7}}{y}

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

2 sin (\frac{π}{6}) \cdot cos (\frac{π}{6}) - 1

(- 1, - 2) y (4, 3)

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