Question

Find z 1 z 2 if z 1 = 3(cos37° + isin37°) and z 2 = (cos53° + isin53°

Answer 1

2i

Explanation:

z 2 = 2/3(cos53° + isin53°

I got it right on odyssey ware

Answer 2

`Z_(1) Z_(2) = 3 i`

Explanation:

Step(i):-

Given z 1 = 3(cos 37° + i sin 37°)

z 2 = (cos 53° + i sin 53°)

by using complex numbers

`Z_(1) = r_(1) ( cos\alpha_(1) + isin\alpha_(1) ) = r_(1) cis\alpha _(1)`

`Z_(2) = r_(2) ( cos\alpha_(2) + isin\alpha_(2) ) = r_(2) cis\alpha _(2)`

step(ii):-

now

`Z_(1) Z_(2) = r_(1) r_(2) cis (\alpha _(1) + \alpha _(2))`

z ₁ = 3(cos 37° + i sin 37°) = 3 c i s 37°

z ₂ = (cos 53° + i sin 53°) = c i s 53°

we will use formula

`Z_(1) Z_(2) = r_(1) r_(2) cis (\alpha _(1) + \alpha _(2))`

`Z_(1) Z_(2) = 3 X 1 cis (37 + 53) = 3cis (90) = 3 cis((\pi )/(2) )`

`Z_(1) Z_(2) = 3(cos((\pi )/(2) ) + isin((\pi )/(2)))`

`Z_(1) Z_(2) = 3(0 + i (1)) = 3 i`

Conclusion:-

`Z_(1) Z_(2) = 3 i`