Solve frac{1+texttt{i}}{{left(1-itexttt{i}right)}^22}

$$\frac{ 1+ \texttt{i} }{ { \left(1-i \texttt{i} \right) }^{ 22 } }$$

Real Part

$$\frac{1}{4194304} = 2.384185791015625 \times 10^{-7}$$

Solution Steps

Multiply i and i to get -1.

$$Re(\frac{1+i}{\left(1-\left(-1\right)\right)^{22}})$$

The opposite of -1 is 1.

$$Re(\frac{1+i}{\left(1+1\right)^{22}})$$

Add 1 and 1 to get 2.

$$Re(\frac{1+i}{2^{22}})$$

Calculate 2 to the power of 22 and get 4194304.

$$Re(\frac{1+i}{4194304})$$

Divide 1+i by 4194304 to get \frac{1}{4194304}+\frac{1}{4194304}i.

$$Re(\frac{1}{4194304}+\frac{1}{4194304}i)$$

The real part of \frac{1}{4194304}+\frac{1}{4194304}i is \frac{1}{4194304}.

$$\frac{1}{4194304}$$

Evaluate

$$\frac{1}{4194304}+\frac{1}{4194304}i\approx 0.000000238+0.000000238i$$