How to express the complex number in trigonometric form: 5-5i?

Keegan Stevens

Keegan Stevens

Answered question

2023-03-25

How to express the complex number in trigonometric form: 5-5i?

Answer & Explanation

shorteghurlxh0m

shorteghurlxh0m

Beginner2023-03-26Added 10 answers

5 2 ( cos ( - π 4 ) + i sin ( - π 4 ) )
Explanation:
To convert from z = x + i y form to z = r ( cos θ + i sin θ ) form, you need to find r and θ .
r = x 2 + y 2 and tan θ = y x
So, r = 5 2 + ( - 5 ) 2 = 50 = 5 2
tan θ = 5 - 5 tan θ = - 1 θ = - π 4
5 - 5 i = 5 2 ( cos ( - π 4 ) + i sin ( - π 4 ) )
Kieran Orozco

Kieran Orozco

Beginner2023-03-27Added 9 answers

Trigonometric form: 7.07 ( cos 45 - i sin 45 ) Explanation: Z = a + i b = 5 - 5 i . Modulus: | Z | = a 2 + b 2
Modulus: | Z | = 5 2 + ( - 5 ) 2
= 50 7.07 Argument: tan α = | b a | = | 5 - 5 | = 1
α = tan - 1 ( 1 ) = 45 0 ; Z lies on fourth
quadrant. θ = 360 - α = 315 0 or ( - 45 ) 0
as represented in trigonometric form as
Z = | Z | ( cos θ + i sin θ )
Z = 7.07 ( cos 315 + i sin 315 ) or
Z = 7.07 ( cos 45 - i sin 45 )

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