What is (x+3i)^2-(2x-3i)^2 ?

The solution to (x+3i)^2-(2x-3i)^2 is -3x^2+18xi

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simplify (x+3i)^2-(2x-3i)^2

simplify

(x + 3 i)^{2} - (2 x - 3 i)^{2}

- 3 x^{2} + 18 x i

Solution steps

(x + 3 i)^{2} - (2 x - 3 i)^{2}

(x + 3 i)^{2} = x^{2} + 6 x i - 9

(2 x - 3 i)^{2} = 4 x^{2} - 12 x i - 9

= x^{2} + 6 x i - 9 - (4 x^{2} - 12 x i - 9)

Expand

- (4 x^{2} - 12 x i - 9) : - 4 x^{2} + 12 x i + 9

= x^{2} + 6 x i - 9 - 4 x^{2} + 12 x i + 9

Group like terms

= x^{2} - 4 x^{2} + 6 x i + 12 x i - 9 + 9

Add similar elements:

x^{2} - 4 x^{2} = - 3 x^{2}

= - 3 x^{2} + 6 x i + 12 x i - 9 + 9

Add similar elements:

6 x i + 12 x i = 18 x i

= - 3 x^{2} + 18 x i - 9 + 9

Add the numbers:

- 9 + 9 = 0

= - 3 x^{2} + 18 x i

\frac{5 x - 1}{x ^{2} + 2 x - 8} - \frac{6}{x + 4}

3 \frac{1}{4} - 2 \frac{1}{5} + \frac{11}{20}

\frac{- 19.3}{- 151.505} - 10

\frac{4}{2}

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