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If |z1|=6 and z2=4+3i, show that the greatest value of |z1+z2| is 11 and find its least value.

If z is a complex number such that |z-4-3i|=1, find algebraically [i.e. by triangular inequality], the max and min value of |z|.

PQR is an isosceles triangle right-angled at P. If the complex number -3+2i represents Q and 4+5i represents R, find the complex numbers representing the possible solutions of P.

can someone help me, i dont know how to do this. :) http://www.wolframalpha.com/input/?i=integrate+lnx%2Fx http://www.wolframalpha.com/input/?i=integrate+%28x%2F%282x%2B1%29%29

Find the number of arrangements of the letters in the word PENCILS if E precedes I. In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from 5 boys and 4 girls? (7200) In how many of these arrangements does a boy occupy the middle position?

there is a 3 lock code with 8 different letters. suppose the lock operates by holding 3 buttons together so that order is not important. how many codes are possible? why isnt the answer 8C3 x 7C2 x 6C1?

a rectangular table has 6 seats, 4 being on one side and 2 on the opposite side. in how many ways can 6 people be seated if A and B must be on opposite sides?

a group of 3 men and 7 boys include a father and son. from this group, a team consisting of 2 men and 2 boys are to be chosen. how many ways can the team be chosen if the father and son cannot be on the team together?

Find the roots of the equation z^6+z^5+..........+z+1=0. Hence find the exact value of cos2pi/7 + cos4pi/7 + cos6pi/7. So I got up to this step: Sum of roots = 2cos2pi/7 + 2cos4pi/7 + 2cos 6pi/7. What should I do next? Thanks in advanced.

1. if z = x+iy, find a relation between x and y given that re (z-4)/z = 0 2. find the complex number z such that z/(1+z) = 1 + i 3. if z = 1+i is a root of x^2+ax+b=0 find the real numbers a and b 4. given Re(z)= 3Imz, find z if z^2-6i is real.

Discuss the concept that length standards are defined in terms of time in contrast to the original metre standard. SO CONFUSED!

Discuss the effect of the Earth’s orbital motion and its rotational motion on the launch of a rocket Transfer orbits between the Earth and other planets in the solar system can be achieved by using the Earth’s orbital velocity around the Sun. If the rocket is launched against the motion of the...

Newton’s concept of escape velocity was that if a body is launched from a very high building, as the velocity of horizontal launch is increased, the body’s rate of fall would match the Earth’s curvature. The escape velocity was equal to the horizontal velocity needed for the body to stay in...

1. Find the stationary point on the curve y=xe^x and determine its nature. 2. Differentiate e^x(2x+1)

find the coordinates of three points on the parabola x^2 = 4y such that the normals through these three points pass through the point (-12, 15).

Points P(10p, 5p^2) and Q (10q, 5q^2) lie on the parabola x^2=20y. Find the equation of the locus of the midpoint of PQ if pq=-2 I got 10y+20=x^2 the answer is 10y-100=x^2 >:[

the normal at any point P(-8p, -4p^2) on the parabola x^2=-16y cuts the y-axis at thepoint M. find the equation of the locus of the midpoint of PM.

Find the equation of the locus of point R that is the intersection of the normals at P(2p, p^2) and Q(2q, q^2) on the parabola x^2=4y given that pq=-4

differentiate (x^4-1)^9 hence find integral of x^3(x^4-1)^8 dx

Express z in the form x+iy in mod-arg form, hence find the exact values of cos 7pi/12 and sin 7pi/12 = root 8 cis 7pi/12 = root 8 (cos 7pi/12 + i sin 7pi/12) what next ? :O thank you ^_^