Answer:
The complex number z = -5 into its rectangular form
Explanation:
* Lets revise the complex numbers
- If z = r(cos Ф ± i sin Ф), where r cos Ф is the real part and i r sin Ф is the
imaginary part in the polar form
- The value of i = √(-1) ⇒ imaginary number
- Then z = a + bi , where a is the real part and bi is the imaginary part
in the rectangular form
∴ a = r cos Ф and b = r sin Ф
* Lets solve the problem
∵ z = r (cos Ф ± i sin Ф)
∵ z = 5 (cos π + i sin π)
∴ The real part is 5 cos π
∴ The imaginary part is 5 sin π
- Lets find the values of cos π and sin π
∵ The angle of measure π is on the negative part of x axis at the
point (-1 , 0)
∵ x = cos π and y = sin π
∴ cos π = -1
∴ sin π = 0
∴ a = 5(-1) = -5
∴ b = 5(0) = 0
∴ z = -5 + i (0)
* The complex number z = -5 into its rectangular form