What is (5+sqrt(-2))^2 ?

The solution to (5+sqrt(-2))^2 is 23+10sqrt(2)i

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simplify (5+sqrt(-2))^2

simplify

(5 + - 2)^{2}

23 + 102 i

Solution steps

(5 + - 2)^{2}

Apply Perfect Square Formula:

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

(5 + - 2)^{2} = 5^{2} + 2 \cdot 5 - 2 + (- 2)^{2}

= 5^{2} + 2 \cdot 5 - 2 + (- 2)^{2}

5^{2} + 2 \cdot 5 - 2 + (- 2)^{2} = 102 i + 23

= 102 i + 23

Rewrite in standard complex form:

23 + 102 i

= 23 + 102 i

a p^{2} (- a^{2} p^{3})^{2}

2 g - \frac{3}{5} (20 - 3 g) + 12

(- 1) - (- 5)

x + 1 - 1 \cdot x + 1 + 1

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