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Popular >

expand (0.3+0.4i)^4

Solution

expand

(0.3 + 0.4 i)^{4}

Solution

- 0.0527 - 0.0336 i

Solution steps

(0.3 + 0.4 i)^{4}

Apply binomial theorem:

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

a = 0.3, b = 0.4 i

= i = 0 \sum 4 (i 4) \cdot 0. 3^{(4 - i)} (0.4 i)^{i}

Expand summation

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 0. 3^{4} (0.4 i)^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 0. 3^{3} (0.4 i)^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 0. 3^{2} (0.4 i)^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 0. 3^{1} (0.4 i)^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 0. 3^{0} (0.4 i)^{4}

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 0. 3^{4} (0.4 i)^{0} = 0.0081

Simplify

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 0. 3^{3} (0.4 i)^{1} : 0.0432 i

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 0. 3^{2} (0.4 i)^{2} = - 0.0864

Simplify

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 0. 3^{1} (0.4 i)^{3} : - 0.0768 i

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 0. 3^{0} (0.4 i)^{4} = 0.0256

= 0.0081 + 0.0432 i - 0.0864 - 0.0768 i + 0.0256

Simplify

0.0081 + 0.0432 i - 0.0864 - 0.0768 i + 0.0256 : - 0.0527 - 0.0336 i

= - 0.0527 - 0.0336 i

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Frequently Asked Questions (FAQ)

What is expand (0.3+0.4i)^4 ?
The solution to expand (0.3+0.4i)^4 is -0.0527-0.0336i