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Chapter 9: Q. 24 (page 592)

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

3(cos210鈭�+isin210鈭�).

Short Answer

Expert verified

The rectangular form of the complex number3(cos210鈭�+isin210鈭�)is,-2.598-1.5i.

Step by step solution

01

Step 1 Given complex number is,

3(cos210鈭�+isin210鈭�).

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

z=3(cos210鈭�+isin210鈭�)=3(cos180鈭�+30鈭�+isin180鈭�+30鈭�)[cos180鈭�+胃=-cos胃sin180鈭�+胃=-sin胃]z=3-cos30鈭�-sin30鈭�

02

Step 2 Substitute the values of sin 30∘,cos 30∘ in the obtained expression.

z=3-32-i12=-332-i32z=-2.598-1.5i

The rectangular form of the given complex number is,-2.598-1.5i.

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