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Exercises for Question Type 4: For a given complex number, determining the quadrant and finding the argument - IB | RevisionDojo

Question 1

Consider the complex number $z = 2 - 2\sqrt{3}i$ .

Determine the quadrant in which $z$ lies and the argument $\arg(z)$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question 2

Determine the quadrant and argument $\arg(z)$ of the complex number $z = 5 - 5i$ , expressing the argument in radians in the interval $(0,2\pi)$ .

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Question 3

Determine the quadrant and the argument $\arg(z)$ of the complex number $z = 1 + i$ , expressing the argument in radians in the interval $[0, 2\pi)$ .

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Question 4

Determine the quadrant and principal argument $\arg(z)$ of the complex number $z = -\sqrt{3} + \sqrt{3}\,i$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question 5

Consider the complex number $z = 7 + 7\text{i}\sqrt{3}$ .

Determine the quadrant in which $z$ lies and find $\arg(z)$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question 6

Determine the quadrant and principal argument $\arg(z)$ of the complex number $z = 3\sqrt{3} - 3i$ , expressing the argument in radians in the interval $(0,2\pi)$ .

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Question 7

Determine the quadrant and argument $\arg(z)$ of the complex number $z = -\sqrt{3} - i$ , expressing the argument in radians in the interval $(0,2\pi)$ .

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Question 8

Determine the quadrant and the argument $\arg(z)$ of the complex number $z = \sqrt{3} - 3i$ , expressing the argument in radians in the interval $[0, 2\pi)$ .

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Question 9

Determine the quadrant and argument $\arg(z)$ of the complex number $z = -1 + \sqrt{3}\,i$ , expressing the argument in radians in the interval $(0,2\pi)$ .

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Question 10

Determine the quadrant and argument $\arg(z)$ of the complex number $z = -2\sqrt{3} + 2i$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question 11

Determine properties of a complex number including its quadrant and argument within a specified interval.

Determine the quadrant and the argument $\arg(z)$ of the complex number $z = -4 + 4i$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question 12

The question asks to identify the quadrant and calculate the argument of a complex number given in Cartesian form, within a specific interval.

Determine the quadrant and the argument $\arg(z)$ of the complex number $z = -3 - 3\sqrt{3}\,i$ , expressing the argument in radians in the interval $(0, 2\pi)$ .

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Question Type 4: For a given complex number, determining the quadrant and finding the argument Exercises