Consider the complex numbers and .
Sketch and on the Argand diagram below, be sure to include an appropriate scale.
Find the modulus of and .
Find the argument of and .
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Consider the complex numbers and .
Sketch and on the Argand diagram below, be sure to include an appropriate scale.
Find the modulus of and .
Find the argument of and .
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Solve the following equations for
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Let , where and .
Express in the form .
Find the modulus and argument for
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Let , where and .
Express in the form .
Find the modulus and argument for .
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Consider the complex numbers and .
Find
Let and represent the complex conjugates of and , respectively.
Write down and , giving your answers in the form .
Find
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Find all possible real values for and such that
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Consider the complex numbers and .
Find
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It is given that and .
Find
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Find the complex numbers and such that
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Let and .
Find , the angle shown on the diagram below.
Find the area of the triangle formed in the diagram above.
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Let and .
Find .
Sketch on the Argand diagram below.
Let be the angle between and and be the angle between and .
Find the angles and , giving your answers in degrees.
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Let , where .
Write in the form
Determine the conditions under which is purely imaginary.
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Consider the equation
Write down an inequality, in terms of and that shows the equation has no real solutions.
is one solution to the equation
Find the values of and
Let
Find using technology.
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Consider the quadratic equation .
The roots of the equation are and where
Find the value of and .
Sketch and on the Argand diagram below, be sure to include an appropriate scale.
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Consider the complex numbers and .
Find
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Consider the complex numbers and .
Find the modulus and argument of .
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Consider the complex numbers and .
Work out the following:
For part (iii) give your answer in the form , where and are real numbers.
Write down the complex conjugate of and describe the geometrical relationship between and .
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Find all possible real values for and such that
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For a general complex number , where , show that
For the complex numbers and , where , show that
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Consider the complex numbers and .
Find
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Consider the complex numbers and where .
Find the possible values of and .
Using the answers gained in part (a), write down values for and that will satisfy the equation
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Consider the complex numbers .
Represent the complex numbers and on an Argand diagram.
The points and are represented by the points and on the Argand diagram respectively.
Find the angle
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Consider the complex numbers and , where .
Find the possible values of and .
Find the modulus of .
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Let .
Given that , express in the form , where .
Find , giving your answer in the form , where
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Consider the complex number .
Use technology to find the values of and . Give your answers in the form , where .
Draw and on an Argand diagram.
Find the smallest integer such that is a real number.
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Consider the complex numbers and .
Find
The complex numbers and are represented by the points and respectively on an Argand diagram with origin .
Determine whether the angle made by with the positive horizontal axis is greater than or less than the angle made by with the positive horizontal axis. Give a reason for your answer.
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Consider the complex number .
Write down, in terms of ,
In the case where , find the modulus and argument of .
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Consider the complex numbers and .
Express in the form , where .
Find
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Consider a general complex number , where , and .
Show that
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Consider the equation , where , .
Find an expression in terms of and for .
Find in terms of given that is purely real.
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Consider the complex numbers and .
Find the modulus of giving your answer as an exact value.
The argument of is given as , where . Find the value of .
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Consider the complex numbers
Express in the form , where .
In the case where is purely imaginary, represent and on an Argand diagram.
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Consider the complex numbers and where
Find the values of and .
Find the modulus of , giving your answer as an exact value.
Find the argument of , giving your answer in the range .
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Consider the complex numbers and .
Find the values of and such that and .
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Consider the complex numbers , and , where and .
Find the values of and in terms of .
Given that , find the possible values of .
Given additionally that radians correct to 2 decimal places, determine the exact value of .
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Consider the complex number .
Use technology to find the values of and . Give your answers in the form , where .
Draw and on an Argand diagram.
Find the smallest integer such that is purely imaginary.
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