Question

Write the real form of each complex equation.

a. z = 4 cos(theta) + 9i sin(theta)
b. z = 6 cos(theta) + i sin(theta)
c. z = √5 cos(theta) + √10i sin(theta)
d. z = 5 − 2i + 4 cos(theta) + 7i sin(theta)

Answer 1

Explanation:

Given

(a)
`z=4\cos (\theta )+9i\sin (\theta )`

`Re(z)=4\cos \theta`

`Im(z)=9\sin \theta`

(b)
`z=6\cos (\theta )+i\sin (\theta )`

`Re(z)=6\cos \theta`

`Im(z)=\sin \theta`

(c)
`z=√(5)\cos (\theta )+√(10)i\sin (\theta )`

`Re(z)=√(5)\cos (\theta )`

`Im(z)=√(10)\sin (\theta )`

(d)
`z=5-2i+4\cos (\theta )+7i\sin (\theta )`

`z=5+4\cos \theta +i(7\sin \theta -2)`

`Re(z)=5+4\cos \theta`

`Im(z)=7\sin \theta -2`