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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.

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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

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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

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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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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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