simplify | 1/(1+i)|

Solution

simplify

\frac{1}{1 + i}

\frac{1}{2}

Decimal Notation

0.70710 \dots

Solution steps

\frac{1}{1 + i}

Simplify

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

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

Apply complex arithmetic rule:

∣ a + bi ∣ = a^{2} + b^{2}

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

= (\frac{1}{2})^{2} + (- \frac{1}{2})^{2}

(\frac{1}{2})^{2} + (- \frac{1}{2})^{2} = \frac{1}{2}

= \frac{1}{2}

\frac{x ^{- 4}}{x ^{3}}

19 \times 7

8 x^{2} - 18 x + 7

\frac{x ^{12}}{x ^{4}}

\frac{5}{3} \times 4