What is (x+iy)(x+iy) ?

The solution to (x+iy)(x+iy) is (x^2-y^2)+2xyi

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simplify (x+iy)(x+iy)

simplify

(x + i y) (x + i y)

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

Solution steps

(x + i y) (x + i y)

Rewrite

x + i y

in standard complex form:

x + y i

Rewrite

x + i y

in standard complex form:

x + y i

= (x + y i) (x + y i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (xx - yy) + (x y + y x) i

Simplify

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

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

x^{2} + 12 + 36

- 10 \cdot 4

\frac{- 39}{( - 3 )}

(\frac{25}{4})^{- \frac{3}{2}}