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(-8^2+ 9^2))=sqrt 145r1=√−82+92)=√145
r_2=sqrt(4^2+ 6^2) =sqrt 52r2=√42+62=√52
theta_1=tan^-1(9 / -8)~~ 131.63^@, " II quadrant"θ1=tan−1(9−8)≈131.63∘, II quadrant
theta_2=tan^-1(6/ 4)~~ 56.31^@, " I quadrant"θ2=tan−1(64)≈56.31∘, I quadrant
z_1 + z_2 = sqrt 145 cos(131.63) + sqrt 52 cos(56.31) + i (sqrt 145 sin 131.63 + sqrt 52 sin 56.31)z1+z2=√145cos(131.63)+√52cos(56.31)+i(√145sin131.63+√52sin56.31)
=> -8 + 4 + i (9 + 6 )⇒−8+4+i(9+6)
color(crimson)(=> -4 + 15 i⇒−4+15i
