Convert 4(cos 60° + i sin 60°) to a+bi.

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Multiple Choice

Convert 4(cos 60° + i sin 60°) to a+bi.

Explanation:
Think of this in rectangular form: a complex number written as a+bi is just the real part plus the imaginary part. When you have r(cos θ + i sin θ), you convert by multiplying r into the cosine and sine components separately. Here the modulus is 4 and the angle is 60 degrees. Use the standard values cos 60° = 1/2 and sin 60° = √3/2. So: 4(cos 60° + i sin 60°) = 4(1/2 + i√3/2) = 4×1/2 + 4×(i√3/2) = 2 + 2√3 i. Thus the real part is 2 and the imaginary part is 2√3, giving 2 + 2√3 i.

Think of this in rectangular form: a complex number written as a+bi is just the real part plus the imaginary part. When you have r(cos θ + i sin θ), you convert by multiplying r into the cosine and sine components separately.

Here the modulus is 4 and the angle is 60 degrees. Use the standard values cos 60° = 1/2 and sin 60° = √3/2. So:

4(cos 60° + i sin 60°) = 4(1/2 + i√3/2) = 4×1/2 + 4×(i√3/2) = 2 + 2√3 i.

Thus the real part is 2 and the imaginary part is 2√3, giving 2 + 2√3 i.

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