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Popular >

simplify (i+xy)^2

Solution

simplify

(i + x y)^{2}

Solution

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

Solution steps

(i + x y)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

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

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

i^{2} = - 1

2 i x y = 2 x y i

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

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

What is (i+xy)^2 ?
The solution to (i+xy)^2 is (-1+x^2y^2)+2xyi