Chapter 6.6, Problem 73E

Solution

a)

To find: The product of given complex number by using calculator.

The product is $478.11+128.11i$ .

Given information:

The complex numbers are,

  $\begin{array}{c}{z}_1=25\sqrt{2}\left(\cos \left(-\frac{\pi }{4}\right)+i\sin \left(-\frac{\pi }{4}\right)\right)\\ z_2=14\left(\cos \frac{\pi }{3}+i\sin \frac{\pi }{3}\right)\end{array}$

Calculation:

Set your calculator $a+ib$ and RADIAN mode and change the number of decimals to be displayed by selecting $2$ in the FLOAT option as shown below.

  

Enter the product and hit ENTER to obtain the same answer as in Example 3.

  

Therefore, the product is $478.11+128.11i$ .

b)

To find: The product of given complex number by using calculator.

The product is $-0.46-0.12i$ .

Given information:

The complex numbers are,

  $\begin{array}{c}{z}_1=2\sqrt{2}\left(\cos 135°+i\sin 135°\right)\\ z_2=6\left(\cos 300°+i\sin 300°\right)\end{array}$

Calculation:

Set your calculator $a+ib$ and RADIAN mode and change the number of decimals to be displayed by selecting $2$ in the FLOAT option as shown below.

  

Enter the product and hit ENTER to obtain the same answer as in Example 4.

  

Therefore, the product is $-0.46-0.12i$ .

c)

To find: The cube root of given complex number by using calculator.

The required result is $-8$ .

Given information:

The complex number is ${\left(1+i\sqrt{3}\right)}^3$ .

Calculation:

Set your calculator $a+ib$ and RADIAN mode as shown below.

  

Enter the given complex number and hit ENTER to obtain the same answer as in Example 5.

  

Therefore, the required result is $-8$ .