Question

Find the quotient z₁/z₂ of the complex numbers,

z₁=24(cos300°+isin300°) and
z₂=8(cos75°+isin75°).

a) 3(cos225°+isin225°)
b) 3(cos225°+isin75°)
c) 3(cos225°+isin300°)
d) 3(cos225°+isin150°)

Answer 1

The quotient of the given complex numbers z₁ and z₂ in polar form is 3(cos225° + isin225°), which is answer option (a).

Step-by-step explanation:

To find the quotient z₁/z₂ of the complex numbers, we can use the properties of complex numbers in polar form. The division of two complex numbers in polar form is done by dividing their magnitudes and subtracting their angles.

Given:

• z₁ = 24(cos300° + isin300°)
• z₂ = 8(cos75° + isin75°)

The quotient z₁/z₂ is calculated by:

• Magnitude: 24 / 8 = 3
• Angle: 300° - 75° = 225°

Therefore, the quotient is:

3(cos225° + isin225°)

This corresponds to option (a).