Chapter 9.6, Problem 4CFU

To determine

To explain:

The alternative method that gives the same value.

Explanation of Solution

Given information:

Let the complex number is given by $z=a+ib$ .

Consider the complex number $z=a+ib$ ,

The conjugate of $a+ib$ is $a-ib$ .

Hence, the product of z and its conjugate is given by,

  $\sqrt{\left(a+ib\right)\left(a-ib\right)}=\sqrt{a^2+b^2}$ here friends method gives the same answer since $\left|z\right|=\sqrt{a^2+b^2}$ .

By numerical method,

The absolute value of $1+i$ is $\sqrt{1^2+1^2}=\sqrt{a^2}$

By using friends method,

The absolute value is $\sqrt{\left(1+i\right)\left(1-i\right)}=\sqrt{1+1}=\sqrt{2}$ .