Download Manipulate real and complex numbers

Manipulate real and complex numbers
and solve equations.
QUESTION ONE
p
, u = 25 - 30i, w = 2 + 3i
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(a)
Show each of the following complex numbers on an Argand diagram.
Label each clearly
(i) z2
(ii) w, the conjugate of w
(b)
Write u in polar form, rcisq .
u
(c)
Write
in rectangular form, a+ ib.
w
QUESTION TWO
z = 3 cis
(a)
(b)
Write (2 - 3 5)(1+ 2) in the form a + b 3 .
p
-2p
Find 6cis x 5cis
in polar form, rcisq .
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QUESTION THREE
Solve each of the following equations.
(a)
2x +3 = 25
(b)
log 2 ( x 2 - 1) - log 2 ( x + 1) = 3
(c)
z 3 = 8. Give your answers in rectangular form
QUESTION FOUR
(a)
(b)
(c)
Solve the equation x +1 = 5 - 2x . Remember to check your answer.
Find all solutions, real and complex, of the equation x 3 + 6 x - 20 = 0 ,
given that one solution is x = -1+ 3i .
Find the solution of the equation x 2 - 4ax - 8 = 0, where a is an unknown constant.
Use the method of completing the square.
QUESTION FIVE
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(a)
Expand fully (2x - 3y ) using the binomial theorem or Pascal’s Triangle
(b)
(
)
(
Determine the 4th term Ax 5 y 3 of the expansion 3x + 2y
)
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