Complex numbers in algebraic and polar form

9000031207

Level:

Find the algebraic form of the complex number

z = 2 (\cos \frac{3 π}{4} + i \sin \frac{3 π}{4})

- \sqrt{2} + i \sqrt{2}

\sqrt{2} + i \sqrt{2}

\sqrt{2} - i \sqrt{2}

- \sqrt{2} - i \sqrt{2}

9000031208

Level:

Find the polar form of the complex number

z = - 3 + 3 i

3 \sqrt{2} (\cos \frac{3 π}{4} + i \sin \frac{3 π}{4})

3 (\cos \frac{π}{4} + i \sin \frac{π}{4})

3 (\cos \frac{5 π}{4} + i \sin \frac{5 π}{4})

3 \sqrt{2} (\cos \frac{7 π}{4} + i \sin \frac{7 π}{4})

9000031209

Level:

Given complex numbers

z_{1} = 2 \sqrt{2} (\cos \frac{π}{4} + i \sin \frac{π}{4})

and

z_{2} = \sqrt{2} (\cos \frac{7 π}{4} + i \sin \frac{7 π}{4})

, find the product

z_{1} z_{2}

4

4 i

- 4 i

- 4

9000031210

Level:

Given complex numbers

z_{1} = 2 \sqrt{3} (\cos \frac{π}{6} + i \sin \frac{π}{6})

and

z_{2} = \sqrt{3} (\cos \frac{4 π}{3} + i \sin \frac{4 π}{3})

, find the quotient

\frac{z_{1}}{z_{2}}

- \sqrt{3} + i

\sqrt{3} - i

\sqrt{3} + i

- \sqrt{3} - i

9000034807

Level:

Find the polar form of the complex number

z = 2 i

2 (\cos \frac{π}{2} + i \sin \frac{π}{2})

\sqrt{2} (\cos \frac{π}{2} + i \sin \frac{π}{2})

\cos \frac{π}{2} + i \sin \frac{π}{2}

2 (\cos 0 + i \sin 0)

9000034808

Level:

Find the algebraic form of the complex number

z = 2 (\cos π + i \sin π)

- 2

2

- 2 i

2 i

9000034809

Level:

Given complex numbers

z_{1} = 2 (\cos \frac{π}{6} + i \sin \frac{π}{6})

and

z_{2} = \sqrt{3} (\cos \frac{4 π}{3} + i \sin \frac{4 π}{3})

, find the angle in the polar form of the product

z_{1} z_{2}

\frac{3 π}{2}

\frac{2}{9} π

\frac{5}{9} π

3 π

9000034810

Level:

Given complex numbers

z_{1} = 2 (\cos \frac{π}{4} + i \sin \frac{π}{4})

and

z_{2} = \sqrt{2} (\cos \frac{7 π}{4} + i \sin \frac{7 π}{4})

, find the angle in the polar form of the quotient

\frac{z_{1}}{z_{2}}

\frac{π}{2}

- \frac{π}{2}

- \frac{3}{2} π

\frac{3}{2} π

9000035704

Level:

Find the polar form of the complex number

A

graphed in the complex plane as shown in the picture.

z = 2 \sqrt{2} (\cos \frac{3 π}{4} + i \sin \frac{3 π}{4})

z = 2 \sqrt{2} (\cos \frac{π}{4} - i \sin \frac{π}{4})

z = 2 \sqrt{2} (- \cos \frac{π}{4} + i \sin \frac{π}{4})

z = 2 \sqrt{2} (\cos \frac{5 π}{4} + i \sin \frac{5 π}{4})

9000035805

Level:

Given the complex numbers

a = 2 (\cos \frac{2 π}{3} + i \sin \frac{2 π}{3}), b = \sqrt{2} (\cos \frac{3 π}{4} + i \sin \frac{3 π}{4}),

find the product

a b

2 \sqrt{2} (\cos \frac{17 π}{12} + i \sin \frac{17 π}{12})

2 \sqrt{2} (\cos \frac{π}{2} + i \sin \frac{π}{2})

2 \sqrt{2} (\cos \frac{5 π}{7} + i \sin \frac{5 π}{7})

2 \sqrt{2} (\cos \frac{5 π}{12} + i \sin \frac{5 π}{12})

Complex numbers in algebraic and polar form

9000031207

9000031208

9000031209

9000031210

9000034807

9000034808

9000034809

9000034810

9000035704

9000035805

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