simplify (1+3i)^3

Solution

simplify

(1 + 3 i)^{3}

- 26 - 18 i

Solution steps

(1 + 3 i)^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + 3 i)^{3} = 1^{3} + 3 \cdot 1^{2} \cdot 3 i + 3 \cdot 1 \cdot (3 i)^{2} + (3 i)^{3}

= 1^{3} + 3 \cdot 1^{2} \cdot 3 i + 3 \cdot 1 \cdot (3 i)^{2} + (3 i)^{3}

Simplify

1^{3} + 3 \cdot 1^{2} \cdot 3 i + 3 \cdot 1 \cdot (3 i)^{2} + (3 i)^{3} : - 18 i - 26

= - 18 i - 26

Rewrite in standard complex form:

- 26 - 18 i

= - 26 - 18 i

\frac{2}{3} \times \frac{1}{2}

\frac{\frac{1}{x}}{\frac{1}{x}}

lo g_{5} (\frac{1}{250})

\frac{1}{x} + \frac{1}{x ^{2}} + \frac{1}{x ^{3}}

- 2 \times 5