Solve |2/1+i|=

$$| \frac { 2 } { 1 + i } | =$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Multiply both numerator and denominator of \frac{2}{1+i} by the complex conjugate of the denominator, 1-i.

$$|\frac{2\left(1-i\right)}{\left(1+i\right)\left(1-i\right)}|$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$|\frac{2\left(1-i\right)}{1^{2}-i^{2}}|$$

By definition, i^{2} is -1. Calculate the denominator.

$$|\frac{2\left(1-i\right)}{2}|$$

Multiply 2 times 1-i.

$$|\frac{2\times 1+2\left(-i\right)}{2}|$$

Do the multiplications in 2\times 1+2\left(-i\right).

$$|\frac{2-2i}{2}|$$

Divide 2-2i by 2 to get 1-i.

$$|1-i|$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 1-i is \sqrt{2}.

$$\sqrt{2}$$

Real Part

$$\sqrt{2} = 1.414213562$$