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Chapter 9: Q. 11 (page 591)

In Problems 11鈥�22, plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.

1+i

Short Answer

Expert verified

The plot is

The polar form isz=2cos45掳+isin45掳

Step by step solution

01

Step 1. Given information

Complex number is given as1+i

02

Step 2. Plotting graph

Let x=1&y=1

Plot the point as,

03

Step 3. Conversion to polar form

The radius is

|z|=r=x2+y2r=12+12=2

And the argument is

sin胃=yr=12cos胃=xr=12鈬�胃=45鈭�

The polar coordinate is (2,45鈭�)

The polar form is

z=r(cos胃+isin胃)z=2cos45掳+isin45掳

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