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

The solution to (1+i)/i+i/(1-i) is 1/2-i 1/2

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

simplify

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

\frac{1}{2} - i \frac{1}{2}

Solution steps

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

Least Common Multiplier of

i, 1 - i : i (1 - i)

Adjust Fractions based on the LCM

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

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

i (1 - i) : 1 + i

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

(1 + i) (1 - i) = 2

= \frac{2 - 1}{1 + i}

Subtract the numbers:

2 - 1 = 1

= \frac{1}{1 + i}

Rationalize

\frac{1}{1 + i} : \frac{1 - i}{2}

= \frac{1 - i}{2}

Rewrite

\frac{1 - i}{2}

in standard complex form:

\frac{1}{2} - \frac{1}{2} i

= \frac{1}{2} - \frac{1}{2} i

3 x^{2} - 18 x + 225 = 6

104 = 8 x

(4 p + 4)^{2} - 3 (4 p + 4) + 4 = 0

6 = p + 3

6 x^{2} + 13 x - 8 = 0