We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
122
5
avatar

1) For how many real values of c do we have \(\left|\frac12-ci\right| = \frac34\)?

2) Determine the complex number z satisfying the equation \(2z-3\bar{z}=-2-30i\).

 Aug 9, 2019
 #1
avatar+6045 
+1

\(\left|\dfrac 1 2 - c i \right| = \left(\dfrac 1 2 \right)^2 + c^2 = \dfrac 3 4\\ \dfrac 1 4 + c^2 = \dfrac 3 4\\ c^2 = \dfrac 1 2\\ c = \pm \dfrac{1}{\sqrt{2}}\)

 

 

\(2z - 3\bar{z} = -2 - 30i\\ \text{let $z=x+iy$}\\ 2x + i2y - 3x + i3y = -2 - 30i\\ -x+i5y=-2-30i\\ x = 2,~y = -6i\\ z = 2-6i\)

.
 Aug 9, 2019
edited by Rom  Aug 9, 2019
 #2
avatar
0

Bad day at the office Rom ?

Guest Aug 9, 2019
 #4
avatar+6045 
0

any day at an office would be a bad day.

Rom  Aug 9, 2019
 #5
avatar
0

It's just an expression, don't take it literally.

You need to look at Q1 as well.

Guest Aug 9, 2019
 #3
avatar+104937 
+1

2) Let  z  =  a + bi

 

So we have

 

2 (a + bi)  - 3 (a - bi)   =  -2  - 30i      simplify

 

2a + 2bi   - 3a  + 3bi  =   -2  - 30i

 

-1a + 5bi =   -2 - 30i

 

Equate terms

 

-1a   = -2             5bi  = -30i

 

a  =  2           b  = -6

 

So

 

z =  2  -  6i   

 

 

cool cool cool

 Aug 9, 2019

9 Online Users

avatar