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

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

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simplify (x+iy)(x-iy)

simplify

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

x^{2} + y^{2}

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) (a - bi) = a^{2} + b^{2}

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

\frac{4 ( 2 x - 1 )}{3} \leq x + 3

x^{2} - 9 > - x^{2} + 9

5 z^{2} + 2 z + 10 = 0

3 x - 9 x^{2} = - 10

5 x + 8 = 6 x