simplify (4-2i)^3

Solution

simplify

(4 - 2 i)^{3}

16 - 88 i

Solution steps

(4 - 2 i)^{3}

Apply Perfect Cube Formula:

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

(4 - 2 i)^{3} = 4^{3} - 3 \cdot 4^{2} \cdot 2 i + 3 \cdot 4 (2 i)^{2} - (2 i)^{3}

= 4^{3} - 3 \cdot 4^{2} \cdot 2 i + 3 \cdot 4 (2 i)^{2} - (2 i)^{3}

Simplify

4^{3} - 3 \cdot 4^{2} \cdot 2 i + 3 \cdot 4 (2 i)^{2} - (2 i)^{3} : - 88 i + 16

= - 88 i + 16

Rewrite in standard complex form:

16 - 88 i

= 16 - 88 i

x^{2} \cdot (- 2)

(2 x + 3) (4 x^{2} - 6 x + 9) - (2 x) (4 x^{2})

\frac{5 - 3 m}{- 3 m + 5}

9 (x + 1) - 3 (x + 1)^{2}

8 - 18 + 72