Algebra Answers

Write two unit multipliers f or the e quivalence: 60 min = 1 hour.

Evaluate 7i left(−5+2iright)=−14
a.\\(4+35i\\)
b.\\(4-30i\\)
c.\\(4+30i\\)
d.\\(4-35i\\)

If zbase1=1−2i,zbase2=−7+i. Findzbase1−zbase2
If z1=1−2i,z2=−7+i. Findz1−z2z1−z2
a.\\(8-3i\\)
b.\\(-7-2i\\)
c.\\(7+2i\\)
d.\\(8-2i\\)

The length of a textbook

Find the Cartesian equation of the locus of the point P representing the complex number z. Sketch the locus of P in each case.

The cost of each of the components in the production of each size of pizza, and the selling price, is
given in the table below:
Cost of Production(cents)
Selling Size :Base Topping Cooking Labour Selling price($)
Small 32 110 8 200 9.50
Medium 50 175 10 240 11.50
Large 72 250 12 280 13.50
Family 98 345 15 320 17.50

a) Use matrix methods to find the total cost of production for each size of the pizzas. Give your
answers in cents?

b) If Profit = Selling price – Cost of Production, write a matrix equation that will enable you to find
the profit and find the profit, in dollars correct to the nearest cent, made on each size of pizza?

A suburban newsagent is asked to collect data about the number of four popular daily newspapers
that he sells in his shop on weekdays.
The number of each paper sold and the daily taking are recorded for Monday to Thursday of the first
week:
Mon 123 108 48 12 348.00
Tue 136 b 43 15 377.60
Wed 115 133 36 11 345.30
Thur 145 128 45 18 405.50
news paper taking:
348.00$
377.60$
345.30$
405.50$
a)(i) Write the number of each paper sold for the four days as a 4 × 4 matrix, P?
(ii)Write the takings for the four days as a column matrix, Q?
b)If newspaper A costs $1.20, newspaper B costs $1.00, newspaper C costs $1.30 and newspaper D
Costs $2.50 write a suitable matrix X, representing the cost of each of the newspapers?
c)Using matrix equation PX=Q to find the missing figure b; the number of newspaper B sold on
Tuesday. Show all working?

when will you apply compound interest?

Find the Cartesian equation of the locus of the point P representing the complex
number z. Sketch the locus of P in each case.

(a) 2|z + 1| = |z − 2|

(b) |(z + i )/ z - 5 - 2i | = 1

(c) Im (z + (9/z ) ) = 0

let x, y, u, v be real numbers and z, w be complex numbers such that z = x + iy,
w = u+iv. In each case, describe the locus of the point (u, v) in the Argand diagram.
(a) w = z + 4 and

(i) |z| = 3, (ii) arg z = π/3, (iii) |z + 4| = 5,
(iv) y = 4x