What is (1-4i)/(1+4i) ?

The solution to (1-4i)/(1+4i) is -15/17-8/17 i

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simplify (1-4i)/(1+4i)

simplify

\frac{1 - 4 i}{1 + 4 i}

- \frac{15}{17} - \frac{8}{17} i

Solution steps

\frac{1 - 4 i}{1 + 4 i}

Multiply by the conjugate

\frac{1 - 4 i}{1 - 4 i}

= \frac{( 1 - 4 i ) ( 1 - 4 i )}{( 1 + 4 i ) ( 1 - 4 i )}

Simplify

\frac{( 1 - 4 i ) ( 1 - 4 i )}{( 1 + 4 i ) ( 1 - 4 i )} : \frac{- 8 i - 15}{17}

= \frac{- 8 i - 15}{17}

Rewrite in standard complex form:

- \frac{15}{17} - \frac{8}{17} i

= - \frac{15}{17} - \frac{8}{17} i

\frac{sin ( x )}{csc ( x )} + \frac{cos ( x )}{sec ( x )} + \frac{tan ( x )}{cot ( x )}

\frac{10 a ^{3} b}{- 15 a b ^{3}}

(x^{2} - 1) (x - 2)

(x^{2} - 1) (x - 1)

5 \times 1 0^{- 3}