Answer 1

Let z = −8 + 15i

Here a = −8 , b = 15

∴ |z| = `sqrt("a"^2 + "b"^2)`

= `sqrt((-8)^2 + 15^2`

= `sqrt(64 + 225)`

= `sqrt(289)`

= 17

The amplitude z is given by

θ = `pi + tan^-1("a"/"b")`

= `tan^-1(15/(-8)) + pi`

= `-tan^-1(15/8) + pi`   ...[∵ tan^–1(– θ) = – tan^–1θ]

Hence, modulus = 17 and 

amplitude = `-tan^-1(15/8)`