सरल कीजिए :
`{:((i) (9 + 8i)-(7i + 3),(ii) (3-4i)+(-4+3i),(iii) (1+i)(1+2i)),((iv) ((4i)/(-i+1))^(2),(v) (cos alpha + i sin alpha)/(cos beta - i sin beta),(vi) (3 + 2i)(2-4i)):}`

Simplify ((cos alpha + i sin alpha)^(4))/(sin beta + i cos beta)^(8)

Express the following in a + ib form: ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5))

(v) (1-i) ^ (2) (1 + i) - (3-4i) ^ (2)

Express the following in a + ib form: (a) ((cos alpha + i sin alpha)^(4))/((sin beta + i cos beta)^(5)) (b) ((1+ cos phi + i sin phi)/(1 + cos phi - isin phi))^(n) (c) ((cos alpha + i sin alpha)(cos beta + i sin beta))/((cos gamma + i sin gamma)(cos delta + i sin delta))

Express the following in a+ib form: ((cos alpha+i sin alpha)^(4))/((sin beta+i cos beta)^(5))

If ((4i^(3)-i)/(2i+1))^(2)=r(cos theta+isin theta) , then cos theta+sin theta is equal to (where, i^(2)=-1 )

If ((4i^(3)-i)/(2i+1))^(2)=r(cos theta+isin theta) , then cos theta+sin theta is equal to (where, i^(2)=-1 )

If (2+i)r^(-1)={4i+(1+i)^(2)}(cos theta+i sin theta) then value of r is