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Popular >

simplify (3+3i)^8

Solution

simplify

(3 + 3 i)^{8}

Solution

104976

Solution steps

(3 + 3 i)^{8}

Apply binomial theorem:

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

a = 3, b = 3 i

= i = 0 \sum 8 (i 8) \cdot 3^{(8 - i)} (3 i)^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 3^{8} (3 i)^{0} : 6561

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 3^{7} (3 i)^{1} : 52488 i

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 3^{6} (3 i)^{2} : 183708 i^{2}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 3^{5} (3 i)^{3} : 367416 i^{3}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 3^{4} (3 i)^{4} : 459270 i^{4}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 3^{3} (3 i)^{5} : 367416 i^{5}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 3^{2} (3 i)^{6} : 183708 i^{6}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 3^{1} (3 i)^{7} : 52488 i^{7}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 3^{0} (3 i)^{8} : 6561 i^{8}

= 6561 + 52488 i + 183708 i^{2} + 367416 i^{3} + 459270 i^{4} + 367416 i^{5} + 183708 i^{6} + 52488 i^{7} + 6561 i^{8}

Simplify

6561 + 52488 i + 183708 i^{2} + 367416 i^{3} + 459270 i^{4} + 367416 i^{5} + 183708 i^{6} + 52488 i^{7} + 6561 i^{8} : 104976

= 104976

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Frequently Asked Questions (FAQ)

What is (3+3i)^8 ?
The solution to (3+3i)^8 is 104976