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Chapter 9: Q. 30 (page 592)

In Problems 23-32, write each complex number in rectangular form.

0.4cos200鈭�+isin200鈭�.

Short Answer

Expert verified

The rectangular form of the complex number0.4cos200鈭�+isin200鈭�is,-0.3758-0.1368i.

Step by step solution

01

Step 1 Given complex number is,

0.4cos200鈭�+isin200鈭�.

We can simplify the terms inside the brackets and write it in the rectangular form.

z=0.4cos200鈭�+isin200鈭�z=0.4cos180鈭�+20鈭�+isin180鈭�+20鈭�z=0.4-cos20鈭�-isin20鈭�[cos180鈭�+胃=-cos胃sin180鈭�+胃=-sin胃]

02

Step 2 Now substitute the values for cos 20∘,sin 20∘.

z=0.4-0.9396-0.342iz=-0.3758-0.1368i

Thus the required rectangular form is,-0.3758-0.1368i.

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