What is (1+isqrt(3))^2 ?

The solution to (1+isqrt(3))^2 is -2+2sqrt(3)i

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simplify (1+isqrt(3))^2

simplify

(1 + i 3)^{2}

- 2 + 23 i

Solution steps

(1 + i 3)^{2}

Apply Perfect Square Formula:

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

(1 + i 3)^{2} = 1^{2} + 2 \cdot 1 i 3 + (i 3)^{2}

= 1^{2} + 2 \cdot 1 i 3 + (i 3)^{2}

Simplify

1^{2} + 2 \cdot 1 i 3 + (i 3)^{2} : 23 i - 2

= 23 i - 2

Rewrite in standard complex form:

- 2 + 23 i

= - 2 + 23 i

(- 6) (- 3)

4 x^{2} + 8 x - 4 - (3 x^{2} + 6 x - 2)

2 x^{2} (3 x - 5 y)

\frac{5}{4} + \frac{7}{12}