More Complexity
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Answer the following questions without the use of a calculator or computer. Briefly explain your answers.
Complex numbers
- Determine the real and imaginary parts of 1/(e^{j3\pi/4}{+}{1\over\sqrt2}e^{j\pi/2})
- Determine the real and imaginary parts of (1-j\sqrt3)^{12}
- Determine the real and imaginary parts of j^j
Complex exponentials
- Determine the real and imaginary parts of (1{+}j)e^{j\omega t}.
- Determine the real and imaginary parts of e^{j\pi/2}e^{j\omega t}.
- Determine the real and imaginary parts of (\cos(\omega t){+}j\sin(\omega t))^n where n is an integer.
- Find a complex number c so that Re(ce^{j\omega t})=A\cos(\omega t)+B\sin(\omega t) for all real numbers \omega and t.
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