Tough questions!!!

Provide accurate answers and illustrations! Also make sure you are familiar with the unit.

1.46 is the value of a+ b+ c in the function f(x)=7x²-6x+1. Determine the Taylor series at x=2.

2.Determine the equivalent of log6+i.

3.Solve for the inverse of (log3+i)/log2

4.What is the representation ofiⁱin terms of e?

5.Re(z)-Im(z) equals to 1 for complex numbers z where z+z is the root of x²-10x+16=0. Determine the equation with roots Re(z) and Im(z)

6.Determine the equation satisfied where|z| equals10^1/2 .

7.For complex numbers, the value of |x+iy| equals 29^1/2. Determine the two numbers which are conjugates of each other.

8.Determine in the Argand plane the hyperbola represented by z²+z²=2.

9.Taking z_k=cos(3k/10)+isin(2k/10) and in the assumption that k=1,2,...9, what can we say about z_k?

10. Solve(-1/2+i3/2)⁶³⁷+(-1/2-i3/2)³³⁷.