What is (1+i)(5-i)^4 ?

The solution to (1+i)(5-i)^4 is 956-4i

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simplify (1+i)(5-i)^4

simplify

(1 + i) (5 - i)^{4}

956 - 4 i

Solution steps

(1 + i) (5 - i)^{4}

= (5 - i)^{4} (1 + i)

Apply the distributive law:

a (b + c) = ab + a c

(5 - i)^{4} (1 + i) = (5 - i)^{4} \cdot 1 + (5 - i)^{4} i

= (5 - i)^{4} \cdot 1 + (5 - i)^{4} i

Simplify

(5 - i)^{4} \cdot 1 + (5 - i)^{4} i : - 4 i + 956

= - 4 i + 956

Rewrite in standard complex form:

956 - 4 i

= 956 - 4 i

(4 - x) (4 + 2 x) (4 - x)

\frac{2 - 5}{2 + 5}

(\frac{2}{7})^{5}

(4 y + 1)^{3}