Question

Find the two square complex roots of z = − √ 4 + √ 4 i . Express your answer in polar form and then convert them into rectangular form. roots: θ 1 < θ 2 z 1 = r 1 cis ( θ 1 ) = a 1 + b 1 i Trig form: ( cis ) Standard form: + i z 2 = r 2 cis ( θ 2 ) = a 2 + b 2 i Trig form: ( cis ) Standard form: + i

Name: find the two square complex roots of z 4 4 i express your answer in polar form and then convert them into rectangular form roots 1 2 z 1 r 1 cis 1 a 1 b 1 i trig form cis standard form i z 2 r 2 cis 2
Uploaded: 2023-05-11T03:27:14-08:00
Duration: 4 min 38 s
Channel: Danielle Fairburn
Description: find the two square complex roots of z 4 4 i express your answer in polar form and then convert them into rectangular form roots 1 2 z 1 r 1 cis 1 a 1 b 1 i trig form cis standard form i z 2 r 2 cis 2

          Find the two square complex roots of  
z
=
−
√
4
+
√
4
i
  . Express your answer in polar form and then convert them into rectangular form.

roots:  
θ
1
<
θ
2
  

  
z
1
=
r
1
cis
(
θ
1
)
=
a
1
+
b
1
i
      

Trig form: 
   ( 
cis
   
 
   )

Standard form: 
    
+
   
 
    
i
 
  
z
2
=
r
2
cis
(
θ
2
)
=
a
2
+
b
2
i
 
Trig form: 
   ( 
cis
 
   )

Standard form: 
   + 
    
i

Added by Ahmad K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Danielle Fairburn

05/11/2023

Step 1

Step 1: Convert z to polar form z = -√4 + √4i r = |z| = √((-√4)² + (√4)²) = √(4 + 4) = √8 θ = arctan(Im(z)/Re(z)) = arctan(√4/-√4) = arctan(-1) = -π/4 So, z = √8 cis(-π/4) Show more…

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Find the two square complex roots of z = − √ 4 + √ 4 i . Express your answer in polar form and then convert them into rectangular form. roots: θ 1 < θ 2 z 1 = r 1 cis ( θ 1 ) = a 1 + b 1 i Trig form: ( cis ) Standard form: + i z 2 = r 2 cis ( θ 2 ) = a 2 + b 2 i Trig form: ( cis ) Standard form: + i