Mathematics Extension 2 Complex Numbers - School of ... · Web viewMathematics Extension 2 Complex...
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ONLINE: MATHEMATICS EXTENSION 2 Topic 2 COMPLEX NUMBERS EXERCISE p2201 p001 Given the two complex numbers find the real part, imaginary part, modulus and argument for each of the following complex numbers: Locate the results on Argand diagrams. physics.usyd.edu.au/teach_res/hsp/math/math.htm p2201 1
Transcript of Mathematics Extension 2 Complex Numbers - School of ... · Web viewMathematics Extension 2 Complex...
ONLINE: MATHEMATICS EXTENSION 2Topic 2 COMPLEX NUMBERS
EXERCISE p2201
p001
Given the two complex numbers
find the real part, imaginary part, modulus and argument for each of the following complex numbers:
Locate the results on Argand diagrams.
physics.usyd.edu.au/teach_res/hsp/math/math.htm p2201 1
p002
Given the two complex numbers
find the real part, imaginary part, modulus and argument for each of the following complex numbers:
Locate the results on Argand diagrams.
p003
Prove that
p004
Prove that
physics.usyd.edu.au/teach_res/hsp/math/math.htm p2201 2
p005
Express the following in rectangular form for k = 0, 2, ,3, .., , 8.
Plot the complex numbers on an Argand diagram.
p006
Prove the following using the properties of complex numbers
p007
Form the product z1 z2 and the quotient z1 / z2 for
physics.usyd.edu.au/teach_res/hsp/math/math.htm p2201 3
ANSWERSa001
(a)
Given the two complex numbers
find the real part, imaginary part, modulus and argument for each of the following complex numbers:
Locate the results on Argand diagrams.
know
Rectangular form
Polar form
Exponential form
Modulus
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Argument
Real part
Imaginary part
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z Re(z) = x Im(z) = y |z| = R Arg(z) = rad
Arg(z) = deg
1.7321 1.0000 2.0000 / 6 301.7321 -1.0000 2.0000 - / 6 - 301.5000 2.5981 3.0000 / 3 601.5000 -2.5981 3.0000 - / 3 - 603.2321 3.5981 4.8366 0.8389 48.073.2321 -1.5981 3.6056 -0.4592 - 26.310.2321 -1.5981 1.6148 -1.4266 - 81.740.2321 3.5981 3.6056 1.5064 86.310 6.0000 6.0000 / 2 905.1962 -3.0000 6.0000 - / 6 - 300.5774 -0.3333 0.6667 - / 6 - 300 0.6667 0.6667 / 2 90
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a002
Given the two complex numbers find the real part, imaginary part, modulus and argument for each of the following complex numbers:
Locate the results on Argand diagrams.
z Re(z) = x Im(z) = y |z| = R Arg(z) = rad
Arg(z) = deg
-2.1213 2.21213 3.0000 - 3 / 4 135.00-2.1213 -2.1213 3.0000 - / 4 - 45.00-1.7321 -1.0000 2.0000 - 5 /6 -150.00-1.7321 -2.5981 1.0000 / 4 45.00-3.8534 1.1213 4.0132 2.8584 163.78-0.3893 3.1455 3.1455 1.6949 97.115.7956 -1.5529 6.0000 - 0.2618 -15.000.3882 -1.4489 1.5000 -1.3090 - 75.00
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a003
Prove that
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a004
Prove that
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a005Express the following in rectangular form for k = 0, 2, ,3, .., , 8.
Plot the complex numbers on an Argand diagram.
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physics.usyd.edu.au/teach_res/hsp/math/math.htm p2201 16
a006
Prove the following using the properties of complex numbers
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a007
Form the product z1 z2 and the quotient z1 / z2 for
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