Your employer automatically puts 5 percent of your salary into a 401(k) retirement account each year. The account earns 10% interest. Suppose you just got the job, your starting salary is $60000, and you expect to receive a 2.5% raise each year. For simplicity, assume that interest earned and your raises are given as nominal rates and compound continuously. Find the value of your retirement account after 20 years

Compute the principal values of i¹² (i — 1)² and (i(i − 1))². - -

1 2 3 Consider the matrix A = 0 4 5. Give an example of 006 (a) a nonzero matrix B for which det(A + B) = det(A) + det(B); (b) a matrix C for which det(A+C)det(A) + det(C).

Find all points at which f(z) = y² sin x + iy is analytic.

Find all the values of 1-i.

1. e² = 1+i. 2. cos z=3+ 4i Determine all complex numbers z such that

Q4*) (make sure you first understand question P5) Discuss the extremisation of the integral I = = √(2(y + 2) ³y' + (x − 7)) c You may find point (iv) in § 3.5 relevant. dx.

Q6*) Describe the plane paths of light in the two-dimensional media in which the light velocities are given respectively by (a) c = a/y, (b) c = a/√y, where a > 0, y > 0.

lim 1 x→0x3 3 So²² 6 tln(1+t) t4 +4 .dt 2