De Moivre's theorem states that for any complex number z = r [ cos(θ) + i sin(θ) ], $$z^n$$ is

r n [ cos(θ n ) + i sin(θ n ) ]

if z = $$\sqrt[]{3}$$ (cos $$\frac{\pi}{5}$$ -i sin $$\frac{\pi}{5}$$ ), $$\left|z\right|$$ & arg z are?

$$\left|z\right|$$ = $$\sqrt[]{3}$$ , arg z = $$\frac{-\pi}{5}$$

$$\left|z\right|$$ =3, arg z = $$\frac{\pi}{5}$$

$$\left|z\right|$$ = $$\sqrt[]{3}$$ , arg z = $$\frac{\pi}{5}$$

$$\left|z\right|$$ = $$\frac{-\pi}{5}$$ , arg z = $$\sqrt[]{3}$$

if z = $$\sqrt[]{3}$$ (cos $$\frac{\pi}{2}$$ + i sin $$\frac{\pi}{2}$$ ), $$z^2$$ is

$$\sqrt[]{3}$$ + $$\frac{i}{2}$$

if $$\left|z\right|$$ = 5 & arg z = $$-\frac{\pi}{3}$$ , what is the polar form of z?

5(cos $$\frac{\pi}{3}$$ - i sin $$\frac{\pi}{3}$$ )

5 (sin $$\frac{\pi}{3}$$ + i cos $$\frac{\pi}{3}$$ )

5sin $$\frac{\pi}{3}$$ - 5cos $$\frac{\pi}{3}$$ i

5(sin $$\frac{\pi}{3}$$ - i cos $$\frac{\pi}{3}$$ )

MORE COMPLEX NUMBERS

Quiz

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

Maths MD

Used 19+ times

FREE Resource

10 questions

Show all answers

1.

FILL IN THE BLANK QUESTION

45 sec • 1 pt

Write the complex number shown in the graph.

2.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

10

4

2

4.

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

r [ ncos(θ) + i nsin(θ) ]

r [ cos(nθ) + i sin(nθ) ]

rⁿ [ cos(nθ) + i sin(nθ) ]

rⁿ [ cos(θⁿ) + i sin(θⁿ) ]

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

1

13

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

What is the principal argument of -2+2i ?

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