Chapter 8.3, Problem 15E

To determine

To calculate: To sketch the complex number $z$ and also sketch $2z,-z,\frac{1}{2}z$ on the same complex plane

Answer to Problem 15E

Complex numbers are sketched on complex plane

Explanation of Solution

Given information: Complex number is $z=1+i$

Formula Used:

Complex number is a number that can be expressed in the form of $a+bi$ , where $a$ and $b$ are real numbers

  $z=a+bi$

Calculation:

Complex number is given as

  $z=1+i$

Value of below complex numbers are:

  $2z=2\left(1+i\right)=2+2i$

  $-z=-\left(1+i\right)=-1-i$

  $\frac{1}{2}z=\frac{1}{2}\left(1+i\right)=\frac{1}{2}+\frac{1}{2}i$

On comparing the above complex numbers with standard form $z=a+bi$ ,

For complex number $z=1+i$

  $\begin{array}{l}a=1\\ b=1\end{array}$

For complex number $2z=2+2i$

  $\begin{array}{l}a=2\\ b=2\end{array}$

For complex number $-z=-1-i$

  $\begin{array}{l}a=-1\\ b=-1\end{array}$

For complex number $\frac{1}{2}z=\frac{1}{2}+\frac{1}{2}i$

  $\begin{array}{l}a=\frac{1}{2}\\ b=\frac{1}{2}\end{array}$

In order to graph the complex number, plot $\left(1,1\right)$ , $\left(2,2\right)$ $\left(-1,-1\right)$ and $\left(\frac{1}{2},\frac{1}{2}\right)$ on the complex plane

  

Conclusion:

Hence, complex numbers are sketched