How do you add $(-7+9i)$ and $(-1+6i)$ in trigonometric form?

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Answer 1 · 2018-07-09T11:27:26

$color(indigo)(=> -8+ 15i$

$z= a+bi= r (costheta+isintheta)$

$r=sqrt(a^2+b^2), " " theta=tan^-1(b/a)$

$r_1(cos(theta_1)+isin(theta_2))+r_2(cos(theta_2)+isin(theta_2))=r_1cos(theta_1)+r_2cos(theta_2)+i(r_1sin(theta_1)+r_2sin(theta_2))$

$r_1=sqrt(-7^2+ 9^2))=sqrt 130$
$r_2=sqrt(-1^2+ 6^2) =sqrt 37$

$theta_1=tan^-1(9 / -7)~~ 127.87^@, " II quadrant"$
$theta_2=tan^-1(6/ -1)~~ 333.43^@, " II quadrant"$

$z_1 + z_2 = sqrt 130 cos(127.87) + sqrt 37 cos(99.46) + i (sqrt 130 sin 127.87 + sqrt 37 sin 99.46)$

$=> -7 - 1 + i (9 + 6 )$

$color(indigo)(=> -8+ 15i$

How do you add (-7+9i)(-7+9i) and (-1+6i)(-1+6i) in trigonometric form?