Question

Let z=3(cos(15°)+isin(15°)), W= 5(cos(54°+isin(54°)). Then zw can be expressed as r(cosα°+isinβ°),where r is a real number,0≤α≤90 and 0≤β≤90.what is r+α+β?

Answer 1

`r=15, alpha=69^@`

Explanation:

`z=3cis15^@`
`w=5cis54^@`
`zw=3cis15^@xx5cis54^@`

`=3xx5xxcis15^@xxcis54^@`
`3xx5=15`
`cis15^@xxcis54^@=cis(15^@+54^@)`
`15^@+54^@=69^@`
`cis(15^@+54^@)=cis69^@`
`cis15^@xxcis54^@=cis69^@`
`3xx5xxcis15^@xxcis54^@=15cis69^@`
`3cis15^@xx5cis54^@=15cis69^@`

`zw=15cis69^@`

Let `rcis(alpha)=15cis69^@`
`r=15, alpha=69^@`