Find the complex conjugate of the complex number (z = 3costheta + 3isintheta) where (theta = frac{pi}{6}).

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Accepted Answer

Step:1 ：Step 1: Replace (theta) with (frac{pi}{6}) in (z), we get (z = 3cosfrac{pi}{6} + 3isinfrac{pi}{6} = frac{3sqrt{3}}{2} + frac{3i}{2})Step:2 ：Step 2: The complex conjugate of a complex number (z = a + bi) is given by (bar{z} = a - bi).Step:3 ：Step 3: Applying this to our complex number, we get (bar{z} = frac{3sqrt{3}}{2} - frac{3i}{2})

Answer

Step: 1 ：Step 1: Replace (theta) with (frac{pi}{6}) in (z), we get (z = 3cosfrac{pi}{6} + 3isinfrac{pi}{6} = frac{3sqrt{3}}{2} + frac{3i}{2})Step: 2 ：Step 2: The complex conjugate of a complex number (z = a + bi) is given by (bar{z} = a - bi).Step: 3 ：Step 3: Applying this to our complex number, we get (bar{z} = frac{3sqrt{3}}{2} - frac{3i}{2})

Find the complex conjugate of the complex number \(z = 3\cos\theta + 3i\sin\theta\) where \(\theta = \frac{\pi}{6}\).

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