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

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

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

simplify

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

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

Solution steps

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

Simplify

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

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

Simplify

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

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

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

Apply the fraction rule:

\frac{a}{a} = 1

\frac{2}{2} = 1

= 1 \cdot (\frac{1}{2} - \frac{1}{2} i)

Apply rule:

1 \cdot a = a

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

\frac{11 !}{3 ! 8 !}

ln (4)

\frac{5 x}{3} - x = \frac{x}{15} - \frac{9}{5}

(x + 5) \geq 3

(15)^{2} = (23)^{2} + x^{2}