AMC12 Complex Numbers

Question 1

If z = 3 + 4i, what is |z|, the modulus of z?

Accepted Answer

5

Answer

7

Answer

25

Answer

4

Question 2

What is the product (2 + 3i)(1 − 2i)?

Accepted Answer

8 − i

Answer

2 − i

Answer

−4 + 7i

Answer

8 + i

Question 3

What is i^23?

Accepted Answer

−i

Answer

1

Answer

i

Answer

−1

Question 4

If z = 1 + i, what is z^4?

Accepted Answer

−4

Answer

4

Answer

4i

Answer

−4i

Question 5

What is the real part of (3 + 4i) / (1 + 2i)?

Accepted Answer

11/5

Answer

3/5

Answer

−1/5

Answer

2

Question 6

If z₁ = 1 + 2i and z₂ = 2 − i, what is z₁ + z₂?

Accepted Answer

3 + i

Answer

3 − i

Answer

−1 + 3i

Answer

1 + 3i

Question 7

If z = cos(π/6) + i·sin(π/6), what is z + z̄ (z plus its complex conjugate)?

Accepted Answer

√3

Answer

0

Answer

1

Answer

2