Question

Use a scientific calculator or unit circle to convert the polar form of the complex number to its equivalent rectangular form. z = 5(cos90° + isin90°)

A) 0 + 5i
B) -5 + 0i
C) 0 - 5i
D) 5 + 0i

Answer 1

To convert the polar form z = 5(cos90° + isin90°) to its rectangular form, we calculate the real part (x-component) as 5*cos90° = 0 and the imaginary part (y-component) as 5*sin90° = 5. Thus, the rectangular form is 0 + 5i, which is option (A).

Step-by-step explanation:

To convert the polar form of the complex number z = 5(cos90° + isin90°) to its equivalent rectangular form, we can use the definition of polar coordinates in terms of rectangular coordinates. In a complex number, the polar form z = r(cosθ + isinθ) can be converted by recognizing that cosθ corresponds to the x-component and sinθ corresponds to the y-component of the rectangular form.

For the given complex number:

• The radius (r) is 5.
• θ (theta), the angle, is 90°.

Using these values, we can say:

x-component, Re(z) = r*cosθ = 5*cos90° = 5*0 = 0

y-component, Im(z) = r*sinθ = 5*sin90° = 5*1 = 5

Therefore, the rectangular form of the complex number is 0 + 5i, which corresponds to option (A).