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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

Popular Examples

expand (1-sin(x))^2 expand

(1 - sin (x))^{2}

expand 1/((1-x)^2)expand

\frac{1}{( 1 - x ) ^{2}}

expand (n(n+1)(2n+1))/6 expand

\frac{n ( n + 1 ) ( 2 n + 1 )}{6}

simplify (sqrt(x)-1)^2 simplify

(x - 1)^{2}

simplify (a+bi)^3 simplify

(a + bi)^{3}

Frequently Asked Questions (FAQ)

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