Cartesian arithmetic and conjugates · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Complex arithmetic and conjugates — objective 1

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(19 + 4 i\) and \(\displaystyle w=\)\(2 + 4 i\). Work exactly.

Find Re(z+w).

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

Complex arithmetic and conjugates — objective 1

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(20 + 5 i\) and \(\displaystyle w=\)\(3 + 5 i\). Work exactly.

Find Re(z+w).

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

Complex arithmetic and conjugates — objective 2

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(20 + 5 i\) and \(\displaystyle w=\)\(3 + 5 i\). Work exactly.

Find Im(zw).

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

Complex arithmetic and conjugates — objective 2

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(21 + 2 i\) and \(\displaystyle w=\)\(4 + i\). Work exactly.

Find Im(zw).

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

Complex arithmetic and conjugates — objective 3

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(21 + 2 i\) and \(\displaystyle w=\)\(4 + i\). Work exactly.

Find \(\displaystyle \operatorname{Re}(\frac{z}{w})\).

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

Complex arithmetic and conjugates — objective 3

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(22 + 3 i\) and \(\displaystyle w=\)\(2 + 2 i\). Work exactly.

Find \(\displaystyle \operatorname{Re}(\frac{z}{w})\).

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

Complex arithmetic and conjugates — objective 4

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(22 + 3 i\) and \(\displaystyle w=\)\(2 + 2 i\). Work exactly.

Find \(\displaystyle |z|^{2}\).

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

Complex arithmetic and conjugates — objective 4

Maths4U Original · Short practice

Let \(\displaystyle z=\)\(23 + 4 i\) and \(\displaystyle w=\)\(3 + 3 i\). Work exactly.

Find \(\displaystyle |z|^{2}\).

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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