Solve 1+i/64+(1-i)

$$\frac { 1 + i } { 64 } + ( 1 - i )$$

Evaluate

$$\frac{65}{64}-\frac{63}{64}i=1.015625-0.984375i$$

Solution Steps

Divide 1+i by 64 to get \frac{1}{64}+\frac{1}{64}i.

$$\frac{1}{64}+\frac{1}{64}i+\left(1-i\right)$$

Combine the real and imaginary parts in numbers \frac{1}{64}+\frac{1}{64}i and 1-i.

$$\frac{1}{64}+1+\left(\frac{1}{64}-1\right)i$$

Add \frac{1}{64} to 1. Add \frac{1}{64} to -1.

$$\frac{65}{64}-\frac{63}{64}i$$

Real Part

$$\frac{65}{64} = 1\frac{1}{64} = 1.015625$$

Solution Steps

Divide 1+i by 64 to get \frac{1}{64}+\frac{1}{64}i.

$$Re(\frac{1}{64}+\frac{1}{64}i+\left(1-i\right))$$

Combine the real and imaginary parts in numbers \frac{1}{64}+\frac{1}{64}i and 1-i.

$$Re(\frac{1}{64}+1+\left(\frac{1}{64}-1\right)i)$$

Add \frac{1}{64} to 1. Add \frac{1}{64} to -1.

$$Re(\frac{65}{64}-\frac{63}{64}i)$$

The real part of \frac{65}{64}-\frac{63}{64}i is \frac{65}{64}.

$$\frac{65}{64}$$