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chwala

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## Homework Statement

The complex number ##u## is defined by ## u= 6-3i/1+2i##

i) Showing all your working find the modulus of u and show that the argument is ## -1/2π##

ii) For the complex number Z satisfying ##arg(Z-u)= 1/4π##, find the least possible value of mod | Z |

iii) For complex number Z, satisfying mod | Z-(1+i)u| = 1 find the greatest possible value of | Z |2. Homework Equations 3. The Attempt at a Solution

i) I have no problem with this one

##6-3i/1+2i ×1-2i/1-2i = -3i## next to get argument we shall have ## 0-3i## where sin^-1## (-3/3)=-1##

it follows that ## ∅= -90^0 ## which is equal to ##-1/2π## which is correct answer as per marking scheme

ii) i have a problem here, all the same my attempt

##Z- (6-3i/1+2i)##

= sin^-1 ##(1/√2) ##

this is from sin^-1 ##(1/√2) ## = ##1/4π##

##Z- (6-3i/1+2i)##=##1+i##

##Z##=##1+i+(6-3i/1+2i)##

=##(5/1+2i)##

and

##5/1+2i##

=##1-2i##

and

##|1-2i|=√5##

This is my second attempt

arg ##Z+(1/2π)## =##1/4π##.........

**the correct answer to this problem is**

is ##3/2√2## kindly assist

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