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

Answer:

Step-by-step 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)$z=\sqrt{5}\cos (\theta )+\sqrt{10}i\sin (\theta )$

$Re(z)=\sqrt{5}\cos (\theta )$

$Im(z)=\sqrt{10}\sin (\theta )$

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

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

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

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