Quiz

Q

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Compelx numbers

1. Let \(z_1 = 8 + 3j\) and \(z_2 = 9 - 2j\). Then,

• \(\) \(\mathbf{Re}(z_1) =\)
• \(\) \(\mathbf{Im}(z_1) =\)
• \(\) \(\mathbf{Re}(z_2) =\)
• \(\) \(\mathbf{Im}(z_2) =\)
• \(\) \(z_1 + z_2 =\)
• \(\) \(z_1 \times z_2 =\)

2. Let \(z_1 = 8 + 3j\) and \(z_2 = 9 - 2j\). Then,

• \(\) \(\frac{z_1}{z_2} = \frac{8 + 3j}{9 - 2j} =\)

3. Let \(z_1 = 1 + j\) and \(z_2 = 3 + 3\sqrt{3} 2j\). Obtain the polar form of \(z_1\) and \(z_2\) \(\)

• \(\) \(\left | z_1 \right | =\)
• \(\) \(arg z_1 =\)
• \(\) \(Arg z_1 =\)
• \(\) \(\left | z_2 \right | =\)
• \(\) \(arg z_2 =\)
• \(\) \(Arg z_2 =\)

4. Let \(z_1 = -2 + 2j\) and \(z_2 = 3j\). Find \(z_1z_2\) and \(z_1/z_2\) by using polar form

• (1) Find polar form of \(z_1\) and \(z_2\)
• (2) Find \(z_1z_2\) and \(z_1/z_2\)

5. Find and graph all roots in the complex plane

• (1) \(\sqrt[3]{3+4j}\)
• (2) \(\sqrt[4]{j}\)

A

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Complex numbers

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5.