What is (1+sqrt(3)i)^2 ?

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

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simplify (1+sqrt(3)i)^2

simplify

(1 + 3 i)^{2}

- 2 + 23 i

Solution steps

(1 + 3 i)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

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

= 23 i - 2

Rewrite in standard complex form:

- 2 + 23 i

= - 2 + 23 i

\frac{π}{3} + π

[19 - 4 c] > 8

lo g_{16} (16)

∣ x + 4 ∣ = 9

(210 - 6) (210 + 6)