z= a+bi= r (costheta+isintheta)z=a+bi=r(cosθ+isinθ)
r=sqrt(a^2+b^2), " " theta=tan^-1(b/a)r=√a2+b2, θ=tan−1(ba)
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))r1(cos(θ1)+isin(θ2))+r2(cos(θ2)+isin(θ2))=r1cos(θ1)+r2cos(θ2)+i(r1sin(θ1)+r2sin(θ2))
r_1=sqrt(-2^2+ -3^2))=sqrt 13r1=√−22+−32)=√13
r_2=sqrt(6^2+ -9^2) =sqrt 117r2=√62+−92=√117
theta_1=tan^-1(-3/-2)~~ 236.31^@, " III quadrant"θ1=tan−1(−3−2)≈236.31∘, III quadrant
theta_2=tan^-1(-9/ 6)~~ 303.69^@, " IV quadrant"θ2=tan−1(−96)≈303.69∘, IV quadrant
z_1 + z_2 = sqrt 13 cos(236.31) + sqrt 117 cos(303.69) + i (sqrt 13 sin 236.31 + sqrt 117 sin 303.69)z1+z2=√13cos(236.31)+√117cos(303.69)+i(√13sin236.31+√117sin303.69)
=> -2+ 6 + i (-3 - 9 )⇒−2+6+i(−3−9)
color(blue)(=> 4 - 12 i⇒4−12i
