What is (1/2-1/(sqrt(2))i)^8 ?

The solution to (1/2-1/(sqrt(2))i)^8 is 17/256-7/(16sqrt(2))i

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simplify (1/2-1/(sqrt(2))i)^8

simplify

(\frac{1}{2} - \frac{1}{2} i)^{8}

\frac{17}{256} - \frac{7}{16 2} i

Solution steps

(\frac{1}{2} - \frac{1}{2} i)^{8}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = \frac{1}{2}, b = - \frac{1}{2} i

= i = 0 \sum 8 (i 8) (\frac{1}{2})^{(8 - i)} (- \frac{1}{2} i)^{i}

Expand summation

= \frac{8 !}{0 ! ( 8 - 0 ) !} (\frac{1}{2})^{8} (- \frac{1}{2} i)^{0} + \frac{8 !}{1 ! ( 8 - 1 ) !} (\frac{1}{2})^{7} (- \frac{1}{2} i)^{1} + \frac{8 !}{2 ! ( 8 - 2 ) !} (\frac{1}{2})^{6} (- \frac{1}{2} i)^{2} + \frac{8 !}{3 ! ( 8 - 3 ) !} (\frac{1}{2})^{5} (- \frac{1}{2} i)^{3} + \frac{8 !}{4 ! ( 8 - 4 ) !} (\frac{1}{2})^{4} (- \frac{1}{2} i)^{4} + \frac{8 !}{5 ! ( 8 - 5 ) !} (\frac{1}{2})^{3} (- \frac{1}{2} i)^{5} + \frac{8 !}{6 ! ( 8 - 6 ) !} (\frac{1}{2})^{2} (- \frac{1}{2} i)^{6} + \frac{8 !}{7 ! ( 8 - 7 ) !} (\frac{1}{2})^{1} (- \frac{1}{2} i)^{7} + \frac{8 !}{8 ! ( 8 - 8 ) !} (\frac{1}{2})^{0} (- \frac{1}{2} i)^{8}

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (\frac{1}{2})^{8} (- \frac{1}{2} i)^{0} : \frac{1}{256}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (\frac{1}{2})^{7} (- \frac{1}{2} i)^{1} : - \frac{i}{16 2}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (\frac{1}{2})^{6} (- \frac{1}{2} i)^{2} : \frac{7 i ^{2}}{32}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (\frac{1}{2})^{5} (- \frac{1}{2} i)^{3} : - \frac{7 i ^{3}}{8 2}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (\frac{1}{2})^{4} (- \frac{1}{2} i)^{4} : \frac{35 i ^{4}}{32}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (\frac{1}{2})^{3} (- \frac{1}{2} i)^{5} : - \frac{7 i ^{5}}{4 2}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (\frac{1}{2})^{2} (- \frac{1}{2} i)^{6} : \frac{7 i ^{6}}{8}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (\frac{1}{2})^{1} (- \frac{1}{2} i)^{7} : - \frac{i ^{7}}{2 2}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (\frac{1}{2})^{0} (- \frac{1}{2} i)^{8} : \frac{i ^{8}}{16}

= \frac{1}{256} - \frac{i}{16 2} + \frac{7 i ^{2}}{32} - \frac{7 i ^{3}}{8 2} + \frac{35 i ^{4}}{32} - \frac{7 i ^{5}}{4 2} + \frac{7 i ^{6}}{8} - \frac{i ^{7}}{2 2} + \frac{i ^{8}}{16}

Simplify

\frac{1}{256} - \frac{i}{16 2} + \frac{7 i ^{2}}{32} - \frac{7 i ^{3}}{8 2} + \frac{35 i ^{4}}{32} - \frac{7 i ^{5}}{4 2} + \frac{7 i ^{6}}{8} - \frac{i ^{7}}{2 2} + \frac{i ^{8}}{16} : \frac{17}{256} - \frac{7}{16 2} i

= \frac{17}{256} - \frac{7}{16 2} i

\frac{2}{5} x - 2 > 2

3 x^{2} + 87 = 30 x

- 3 b (b - 2) + 7 (b - 2)^{2}

3 ∣ x + 1 ∣ + 2 = 11

12 x^{2} - 8 x + 1 = 0

What is (1/2-1/(sqrt(2))i)^8 ?
The solution to (1/2-1/(sqrt(2))i)^8 is 17/256-7/(16sqrt(2))i