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Popular >

simplify (x+iy)^2

Solution

simplify

(x + i y)^{2}

Solution

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

Solution steps

(x + i y)^{2}

Apply Perfect Square Formula:

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

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

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

2 x i y = 2 x y i

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

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

Rewrite in standard complex form:

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

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

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Frequently Asked Questions (FAQ)

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