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Chapter 9: Q. 23 (page 592)

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

2cos120鈭�+isin120鈭�.

Short Answer

Expert verified

The rectangular form of2cos120鈭�+isin120鈭�is,-1+3i.

Step by step solution

01

Step 1 The given complex number is,

2cos120鈭�+isin120鈭�.

Ifz=rcos胃+isin胃represents a complex number in polar form, then itsxandycoordinates are,x=rcos胃andy=rsin胃, wherer,胃represents the polar co-ordinates of this point.

02

Step 2 The rectangular form of z is,x+iy.

The xcoordinate of 2cos120鈭�+isin120鈭�is,

role="math" localid="1646718906260" x=rcos胃=2cos120鈭�=2cos-0.5=-1

The yco-ordinate is,

y=rsin胃=2sin120鈭�=2.32=3

Thus,

z=x+iyx=-1+3i

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