Chp 13 Complex Numbers

What is the value of i¹⁰?

• i

• -i

• 1

• -1

Let z = x + yi. Which of the following is true about z*, the complex conjugate of z?

(There may be more than 1 correct answer)

• z + z* = 2x

• z - z* = 2y

• zz* is purely real

• z* = x - iy

• 1 - i

arg (1-i) =

Which of the following properties of |z| are true?

(There are more than 1 answer)

• |z| = |z*|

• |z| = -|z*|

• |z₁z₂| = |z₁||z₂|

• |z|² = zz*

• |zⁿ| = |z|ⁿ

Which of the following properties of arg (z) are true?

(There are more than 1 answer)

• arg(z*) = - arg(z)

• arg (z₁z₂) =

  arg (z₁)+ arg (z₂)

• 0 ≤ arg(z) ≤ 2π

• arg(zⁿ) = n arg(z)

Which equations will have roots occuring in conjugate pairs?

(You can choose more than 1 answer)

• 2z³ + z² +3z +2 =0

• z² + iz +3 = 0

• (ln2)z² + z + 1 =0

• z⁵ + 1 = 0