निम्नलिखित सम्मिश्र संख्याओं को ध्रुवीय रूप में लिखे ।
(i) `sin30^(@)+icos30^(@)` (ii) `1+i`
(iii) `-4+i4sqrt(3)` (iv) `((2+i)/(3-i))^(2)` (v) `(-16)/(1+isqrt(3))` (vi) `(i-1)/(“cos”(pi)/(3)+i “sin”(pi)/(3))`
(vii) `(i-sqrt(3))^(13)` (viii) `-1-isqrt(3)`
(ix) `(-1-sqrt(2)i)`
(x) `3-4i`
(i) `sin30^(@)+icos30^(@)` (ii) `1+i`
(iii) `-4+i4sqrt(3)` (iv) `((2+i)/(3-i))^(2)` (v) `(-16)/(1+isqrt(3))` (vi) `(i-1)/(“cos”(pi)/(3)+i “sin”(pi)/(3))`
(vii) `(i-sqrt(3))^(13)` (viii) `-1-isqrt(3)`
(ix) `(-1-sqrt(2)i)`
(x) `3-4i`
Correct Answer – (i) `”cos”(pi)/(3)+i”sin”(pi)/(3)` (ii) `sqrt(2)(“cos”(pi)/(4)+i “sin”(pi)/(4))` (iii) `8(“cos”(2pi)/(3)+i “sin”(2pi)/(3))` (iv) `(1)/(2)(“cos”(pi)/(2)+i “sin”(pi)/(2))` (v) `8(“cos”(2pi)/(3)+i “sin”(2pi)/(3))` (vi) `sqrt(2)(“cos”(5pi)/(12)+i “sin”(5pi)/(12))` (vii) `8192(cos 150^(@)+i sin150^(@))` (viii) `2(cos240^(@)+isin240^(@))` (ix) `sqrt(3)(costheta+isintheta),theta=tan^(-1)sqrt(2)` (x) `5(costheta-isintheta)` (xi) `sqrt(2)(“cos”(pi)/(4)-i”sin”(pi)/(4))`
(ii) `+i=r(costheta+isintheta)rArrrcostheta=1,rsintheta=1`
`rArr” “tantheta=1,theta=(pi)/(4)` तथा `r=sqrt(2)`
`:.` ध्रुवीय रूप `=sqrt(2)(“cos”(pi)/(4)+i “sin”(pi)/(4))`