*** Using 1 angle find a and c ***

[loco]

The first part of a question I'm trying to tackle says:
Given Z1 = a + i (in cartesian notation) with an angle of theta = pi/4 (in polar notation) and
Z2 = c + i (in cartesian notation) with an angle of theta2 = pi/6 ( in polar notation)

find a and c


How is this question possible when only given 1 angle?

Is there a way to in fact find the values of a and c?

Because at the moment all we know is in cartesian -> a + i in polar -> r,45 degrees
cartesian -> c + i in polar -> r, 30 degrees

Is this enough?

Would be very grateful if someone could show me how to move forward!

 

[pka]

The first part of a question I'm trying to tackle says:
Given Z1 = a + i (in cartesian notation) with an angle of theta = pi/4 (in polar notation) and
Z2 = c + i (in cartesian notation) with an angle of theta2 = pi/6 ( in polar notation)
find a and c

\(\displaystyle \dfrac{1}{a}=\tan\left(\dfrac{\pi}{4}\right)\\ \dfrac{1}{c}=\tan\left( \dfrac{\pi}{6}\right)\)

 

[loco]

thank you !!

 

[loco]

\(\displaystyle \dfrac{1}{a}=\tan\left(\dfrac{\pi}{4}\right)\\ \dfrac{1}{c}=\tan\left( \dfrac{\pi}{6}\right)\)

Does this mean that a = 1 and c = root 3 ?

 

[pka]

does this mean that a = 1 and c = root 3 ?

yes.