What is (a+ibsqrt(5))^2 ?

The solution to (a+ibsqrt(5))^2 is (a^2-5b^2)+2sqrt(5)abi

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simplify (a+ibsqrt(5))^2

simplify

(a + ib 5)^{2}

(a^{2} - 5 b^{2}) + 25 abi

Solution steps

(a + ib 5)^{2}

Apply Perfect Square Formula:

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

(a + ib 5)^{2} = a^{2} + 2 aib 5 + (ib 5)^{2}

= a^{2} + 2 aib 5 + (ib 5)^{2}

2 aib 5 = 25 abi

(ib 5)^{2} = - 5 b^{2}

= a^{2} + 25 abi - 5 b^{2}

Rewrite in standard complex form:

(a^{2} - 5 b^{2}) + 25 abi

= (a^{2} - 5 b^{2}) + 25 abi

s (x) 9000 (1 - e^{- 0.002 x})

\frac{5}{4} (20 x + 12 = - 35)

n \cdot (4 n + 1 + 2 n)

(- 3 - 5) y \frac{B}{( 3.5 )}

y^{\frac{1}{3}} (y^{\frac{1}{3}} - y^{\frac{3}{5}})

What is (a+ibsqrt(5))^2 ?
The solution to (a+ibsqrt(5))^2 is (a^2-5b^2)+2sqrt(5)abi