What is (1-isqrt(2))^2 ?

The solution to (1-isqrt(2))^2 is -1-2sqrt(2)i

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simplify (1-isqrt(2))^2

simplify

(1 - i 2)^{2}

- 1 - 22 i

Solution steps

(1 - i 2)^{2}

Apply Perfect Square Formula:

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

(1 - i 2)^{2} = 1^{2} - 2 \cdot 1 i 2 + (i 2)^{2}

= 1^{2} - 2 \cdot 1 i 2 + (i 2)^{2}

Simplify

1^{2} - 2 \cdot 1 i 2 + (i 2)^{2} : - 22 i - 1

= - 22 i - 1

Rewrite in standard complex form:

- 1 - 22 i

= - 1 - 22 i

(0 - 2)^{2} + (y + 7)^{2} = 9

9 y^{2} - 30 y + 25

6 x^{3} - 11 x^{2} - 10 x

(x y)^{3}

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