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Popular >

simplify 1/(0.1i+1)

Solution

simplify

\frac{1}{0.1 i + 1}

Solution

0.99009 \dots - 0.09900 \dots i

Solution steps

\frac{1}{0.1 i + 1}

Multiply by the conjugate

\frac{1 - 0.1 i}{1 - 0.1 i}

= \frac{1 \cdot ( 1 - 0.1 i )}{( 0.1 i + 1 ) ( 1 - 0.1 i )}

1 \cdot (1 - 0.1 i) = 1 - 0.1 i

(0.1 i + 1) (1 - 0.1 i) = 1.01

= \frac{1 - 0.1 i}{1.01}

Rewrite

\frac{1 - 0.1 i}{1.01}

in standard complex form:

0.99009 \dots - 0.09900 \dots i

= 0.99009 \dots - 0.09900 \dots i

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Frequently Asked Questions (FAQ)

What is 1/(0.1i+1) ?
The solution to 1/(0.1i+1) is 0.99009…-0.09900…i