What is ((2+sqrt(-3))/2)((2-sqrt(-3))/2) ?

The solution to ((2+sqrt(-3))/2)((2-sqrt(-3))/2) is 7/4

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simplify ((2+sqrt(-3))/2)((2-sqrt(-3))/2)

simplify

(\frac{2 + - 3}{2}) (\frac{2 - - 3}{2})

\frac{7}{4}

Solution steps

(\frac{2 + - 3}{2}) (\frac{2 - - 3}{2})

(\frac{2 + - 3}{2}) (\frac{2 - - 3}{2}) = \frac{2 + - 3}{2} \cdot \frac{2 - - 3}{2}

= \frac{2 + - 3}{2} \cdot \frac{2 - - 3}{2}

\frac{2 + - 3}{2} = 1 + \frac{3 i}{2}

= (1 + \frac{3 i}{2}) \frac{2 - - 3}{2}

\frac{2 - - 3}{2} = 1 - \frac{3 i}{2}

= (1 + \frac{3 i}{2}) (1 - \frac{3 i}{2})

Rewrite

1 + \frac{3 i}{2}

in standard complex form:

1 + \frac{3}{2} i

Rewrite

1 - \frac{3 i}{2}

in standard complex form:

1 - \frac{3}{2} i

= (1 + \frac{3}{2} i) (1 - \frac{3}{2} i)

Apply complex arithmetic rule:

(a + bi) (a - bi) = a^{2} + b^{2}

= 1^{2} + (\frac{3}{2})^{2}

1^{2} = 1

(\frac{3}{2})^{2} = \frac{3}{4}

= 1 + \frac{3}{4}

1 + \frac{3}{4} = \frac{7}{4}

= \frac{7}{4}

\frac{\frac{1}{x}}{\frac{2}{y}}

\frac{7}{4} = \frac{- 1 + 4 y}{- 5}

\frac{x - 3}{3} = \frac{x - 5}{5}

(11 b^{2} - 4 b + 7) - (b^{2} + 8 b - 9)

8 b^{2} - 10 b + 3 = 0

What is ((2+sqrt(-3))/2)((2-sqrt(-3))/2) ?
The solution to ((2+sqrt(-3))/2)((2-sqrt(-3))/2) is 7/4