Algebra Answers

Suppose that a/c = b/d where a, b, c, and d
d are real numbers. Use both arithmetic and
algebra to show that a/c = a-b/c-d is true.

Find the modulus and the principal argument of each of the given complex numbers.
(a) 3 − 4i, (b) −2 + i, (c) 1
1 + i
√
3
, (d) 7 − i
−4 − 3i
,
(e) 5(cos π/3 + isin π/3), (f) cos 2π/3 − sin 2π/3.

Given that z = 1 + i
√2, express in the form a + ib each of the complex numbers
p = z + 1/z, q = z − 1/z. In an Argand diagram, P and Q are the points which
represent p and q respectively, O is the orgin, M is the midpoint of P Q and G is the
point on OM such that OG =
2
3
OM. Prove that angle P GQ is a right angle.

Given that 3 + i is a root of the equation z
3 − 3z
2 − 8z + 30 = 0, find the
remaining roots.

Show that z = i is a root of the equation z
4 + z
3 + z − 1 = 0. Find the three
other roots.

Them Distributes Three Quad And Five Lined Exercise Books To 37 Learners. How Many Of Each Type Of Exercise Book Has She Distributed

On a long dirt road the bus covered only 6 miles in 10 minutes. At this speed how far would the bus go on 15 minutes explain your answer.

Given that 3 + i is a root of the equation z^3 − 3z^2 − 8z + 30= 0, find the remaining roots.

Show that z = i is a root of the equation z^4 + z^3 + z − 1 = 0. Find the three other roots.

Given that w denotes either one of the non-real roots of the equation z^3 = 1, show
that
(a) 1 + w + w^2 = 0, and
(b) the other non-real root is w^2
. Show that the non-real roots of the equation

((1 − u)÷u)^3
can be expressed in the form Aw and Bw^2
, where A and B are real
numbers, find A and B.