1. What is the conjugate of 1/(1+i)?
2. Find the real and imaginary parts of the Complex number 1/(5+4i).
3. Find the modulus of (3-i)(2+i)/(2-i).
4. If x+iy=3/(2+Cosθ+iSinθ), prove that x²+y² = 4x-3.
5. What is the argument of the complex number -1+i?
6. Find the modulus and argument of the complex number -√6-√2i.
7. If (a+ib) (c+id) = (p+iq), prove that (a²+b²) (c²+d²) = (p²+q²).
8. Express the complex number 2+2√3i in the polar form (that is, in the form aCosθ + ibSinθ.
9. Prove that the points 3+7i, 6+5i, and 15-i are collinear in the Argand plane.
10. Prove that the points representing the complex numbers -1, 3+i, 2+2i, and -2+i on the Argand plane are the vertices of a parallelogram.
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