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Chapter 6: Problem 35

Write each complex number in rectangular form. If necessary, round to the nearest tenth. $$20\left(\cos 205^{\circ}+i \sin 205^{\circ}\right)$$

Short Answer

Expert verified
Using a calculator, the real part a = 20 cos 205掳 = -18.8 approximately and the imaginary part b = 20 sin 205掳 = -6.8 approximately. So, the complex number in rectangular form is \( -18.8 - 6.8i \).

Step by step solution

01

Compute the Real Part

The real part (a) of the complex number is computed by multiplying the modulus with the cosine of the angle. Therefore, \(a = r \cos 胃 = 20 \cos 205掳\).
02

Compute the Imaginary Part

The imaginary part (b) of the complex number is computed by multiplying the modulus with the sine of the angle. Therefore, \(b = r \sin 胃 = 20 \sin 205掳 \).
03

Convert to Rectangular Form

The complex number, in rectangular form, is then represented as a + bi. Therefore, substitute the computed a and b into this equation. If necessary, round the values to the nearest tenth.

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