What is (x+iy)^2+(x-iy)^2 ?

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

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simplify (x+iy)^2+(x-iy)^2

simplify

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

2 x^{2} - 2 y^{2}

Solution steps

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

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

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

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

Group like terms

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

Add similar elements:

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

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

Add similar elements:

2 x y i - 2 x y i = 0

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

Add similar elements:

- y^{2} - y^{2} = - 2 y^{2}

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

0 (- 4)

(1 + 2 i) \cdot (3 + 4 i)

2 ∣ - 2 - 4 ∣ - 3

34 \div 2 \frac{5}{6}

14 x^{3} - 7 x^{2} - 21 x