Values of Expressions with Imaginary Units | math4u.vsb.cz

Submitted by vladimir.arzt on Thu, 05/23/2024 - 17:55

Project ID:

7200000041

Accepted:

SubArea:

Complex numbers in algebraic and polar form

Type:

Layout:

Question:

Match each expression with imaginary units with its value.

Questions Title:

Expressions with imaginary units

Answers Title:

Expression values

Question 1:

i + i^{2} + i^{3} + i^{4} + i^{5} + i^{6}

Answer 1:

i - 1

Question 2:

i \cdot i^{2} \cdot i^{3} \cdot i^{4} \cdot i^{5} \cdot i^{6}

Answer 2:

i

Question 3:

i + i^{3} + i^{5} + i^{7} + i^{9} + i^{11}

Answer 3:

0

Question 4:

i^{2} \cdot i^{4} \cdot i^{6} \cdot i^{8} \cdot i^{10} \cdot i^{12}

Answer 4:

- 1

Question 5:

i^{11} + i^{21} + i^{31} + i^{41} + i^{51}

Answer 5:

$- i$

Question 6:

\frac{1}{i^{12}} + \frac{1}{i^{22}} + \frac{1}{i^{32}} + \frac{1}{i^{42}} + \frac{1}{i^{52}}

Answer 6:

1

Answer 7:

i + 1

Answer 8:

1 - i