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Chapter 9: Q. 26 (page 592)

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

2cos5蟺6+isin5蟺6.

Short Answer

Expert verified

The rectangular form of the complex number2cos5蟺6+isin5蟺6is,-3+i.

Step by step solution

01

Step 1 Given complex number is, 

2cos5蟺6+isin5蟺6.

The given complex number is in the form of z=rcos胃+isin胃.

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

z=2cos5蟺6+isin5蟺6z=2cos蟺2+蟺3+isin蟺2+蟺3z=2-sin蟺3+icos蟺3[sin蟺2+胃=cos胃cos蟺2+胃=-sin胃]

02

Step 2 Now substitute the values of sin π3,cos π3 in the obtained expression.

z=2-32+i12z=-3+i

The rectangular form of the given complex number is,-3+i.

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