How do you multiply (1+3i)(1-3i) in trigonometric form?

1 Answer
George C.
Mar 27, 2016

(1 + 3i)(1 - 3i) = 10

Explanation:

abs(1+3i) = abs(1-3i) = sqrt(1^2+3^2) = sqrt(10)

1 + 3i = sqrt(10) cis (arctan(3))

1 - 3i = sqrt(10) cis (arctan(-3)) = sqrt(10) cis (-arctan(3))

So:

(1 + 3i)(1 - 3i)

= (sqrt(10) cis (arctan(3)))(sqrt(10) cis (-arctan(3)))

= (sqrt(10))^2 cis (arctan(3) - arctan(3))

= 10 cis(0)

= 10

Related questions
See all questions in The Trigonometric Form of Complex Numbers
Impact of this question
1692 views around the world
You can reuse this answer
Creative Commons License