Modulus–argument form and operations · Short practice

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Recall

Modulus and principal argument — objective 1

Maths4U Original · Short practice

Let \(\displaystyle z=2(\cos(- \frac{3 \pi}{4})+i\sin(- \frac{3 \pi}{4}))\). Use principal arguments in (−π,π].

Find |z|.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Modulus and principal argument — objective 1

Maths4U Original · Short practice

Let \(\displaystyle z=3(\cos(\frac{\pi}{6})+i\sin(\frac{\pi}{6}))\). Use principal arguments in (−π,π].

Find |z|.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Method

Modulus and principal argument — objective 2

Maths4U Original · Short practice

Let \(\displaystyle z=3(\cos(\frac{\pi}{6})+i\sin(\frac{\pi}{6}))\). Use principal arguments in (−π,π].

Find arg z divided by π.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Modulus and principal argument — objective 2

Maths4U Original · Short practice

Let \(\displaystyle z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))\). Use principal arguments in (−π,π].

Find arg z divided by π.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Apply

Modulus and principal argument — objective 3

Maths4U Original · Short practice

Let \(\displaystyle z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))\). Use principal arguments in (−π,π].

Find the principal arg(\(\displaystyle z^{2}\)) divided by π.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Modulus and principal argument — objective 3

Maths4U Original · Short practice

Let \(\displaystyle z=5(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3}))\). Use principal arguments in (−π,π].

Find the principal arg(\(\displaystyle z^{2}\)) divided by π.

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Check understanding

Modulus and principal argument — objective 4

Maths4U Original · Short practice

Let \(\displaystyle z=5(\cos(\frac{\pi}{3})+i\sin(\frac{\pi}{3}))\). Use principal arguments in (−π,π].

Find \(\displaystyle |z^{3}|\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

Fresh review variant

Modulus and principal argument — objective 4

Maths4U Original · Short practice

Let \(\displaystyle z=6(\cos(\frac{2 \pi}{3})+i\sin(\frac{2 \pi}{3}))\). Use principal arguments in (−π,π].

Find \(\displaystyle |z^{3}|\).

Enter one number or fraction. Keep exact values during your working; use at least six decimal places for an approximate final answer. A calculator may be used.

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