Question

How do you multiply `(5-i)(6-4i)` in trigonometric form?

Answer 1

`C= sqrt(26)*sqrt(52)/_(349^0+326^0)`
`C~~36.8/_315^0`

Explanation:

Given: `C_1= (5-i), C_2=(6-4i)`

Required: The product of `C_1*C_2` in trigonometric form

Solution Strategy:
1) Convert the Phasors (another name for complex numbers) to their polar or trig form. That is given by:
`C_1 = |C_1| (cos theta +isintheta)`
where: `|C_1|= sqrt(5^2+1^2)=sqrt(26); theta= tan^-1 (-1/5)=349`

`C_2 = |C_2| (cos alpha+isinalpha)`
`|C_2|= sqrt(6^2+4^2)=sqrt(52); theta= tan^-1 (-4/6)=326`

2) Product: `C_1*C_2= sqrt(26)/_349^o*sqrt(52)/_326^o`
`= sqrt(26)*sqrt(52)/_(349^0+326^0)`