How do you multiply (5-i)(6-4i) (5i)(64i) in trigonometric form?

1 Answer
Apr 10, 2016

C= sqrt(26)*sqrt(52)/_(349^0+326^0)C=2652(3490+3260)
C~~36.8/_315^0C36.83150

Explanation:

Given: C_1= (5-i), C_2=(6-4i) C1=(5i),C2=(64i)

Required: The product of C_1*C_2C1C2 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)C1=|C1|(cosθ+isinθ)
where: |C_1|= sqrt(5^2+1^2)=sqrt(26); theta= tan^-1 (-1/5)=349|C1|=52+12=26;θ=tan1(15)=349

C_2 = |C_2| (cos alpha+isinalpha)C2=|C2|(cosα+isinα)
|C_2|= sqrt(6^2+4^2)=sqrt(52); theta= tan^-1 (-4/6)=326|C2|=62+42=52;θ=tan1(46)=326

2) Product: C_1*C_2= sqrt(26)/_349^o*sqrt(52)/_326^oC1C2=26349o52326o
= sqrt(26)*sqrt(52)/_(349^0+326^0)=2652(3490+3260)