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Chapter 6: Problem 36

Write each complex number in rectangular form. If necessary, round to the nearest tenth. $$30(\cos 2.3+i \sin 2.3)$$

Short Answer

Expert verified
The rectangular form of the given complex number can be obtained after calculating the real part \(x\) and the imaginary part \(y\). The resulting rectangular form will be \(x + yi\).

Step by step solution

01

Identify the magnitude and the angle

From the given complex number \(30(\cos 2.3+i \sin 2.3)\), we see that the magnitude r is 30 and the angle 胃 is 2.3.
02

Calculate the real part (x) of the complex number

The real part can be obtained by multiplying the magnitude with cosine of the angle. i.e. \(x = r \cos(胃) = 30 \cos(2.3)\). Now calculate the value of \(30 \cos(2.3)\).
03

Calculate the imaginary part (y) of the complex number

The imaginary part can be obtained by multiplying the magnitude with sine of the angle. i.e. \(y = r \sin(胃) = 30 \sin(2.3)\). Now calculate the value of \(30 \sin(2.3)\).
04

Write the rectangular form of the complex number

The rectangular form of a complex number is expressed as \(x + yi\). Substitute the calculated values of x and y.

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