Chapter 6.5, Problem 50E

To determine

Tofind:The standard form and represent the complex number graphically.

Answer to Problem 50E

The standard form of the number is $1.5i$ .

Explanation of Solution

Given:

  $1.5\left(\text{cos}\frac{\pi }{2}\text{+isin}\frac{\pi }{2}\right)$ .

Concept used:

Standard form of Complex number: $z=a+ib$

Where $a=\text{real number and }b=\text{imaginary number}\text{.}$

To plot the graph:

Step 1. Determine the real and imaginary party of the complex number.

Step2. Move along the horizontal axis to show the real part of the number.

Step3. Move parallel to the vertical to show the imaginary part of the number.

Step4. Plot the point.

Calculation:

  $1.5\left(\text{cos}\frac{\pi }{2}\text{+isin}\frac{\pi }{2}\right)$ .

Here $\cos {90}^0=0$ and $\sin {90}^0=1.$

  $1.5\left(\text{cos}\frac{\pi }{2}\text{+isin}\frac{\pi }{2}\right)=1.5\left(0+i\right)$

  $\Rightarrow 1.5i$

The standard form of the number is $1.5i$ .

The complex number z can be expressed as the point $\left(a,b\right)$ in the complex plane.

The plot of the complex number is shown in below: