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Please answer this question with steps.do I need to use Euler form

Please answer this question with steps.do I need to use Euler form

Question Image
Grade:10

1 Answers

Rajat
213 Points
2 years ago
Let |z|= a, 
So, z/a= ei(π/4) = (1+i)/√2
|z+3-i| = | a(1+i)/√2 + (3-i)| =|(a/√2+3)+I(a/√2-1)|
=4
or, (a/√2+3)2+(a/√2-1)2 =16
or, (a^2/2+9+3√2a)+(a^2/2+1-√2a)=16
or, (a^2 +10+2√2a)=16
or, a^2+2√2a-6=0
or, a^2+3√2a-√2a-6=0
or, a(a+3√2)-√2(a+3√2)=0
or, (a+3√2)(a-√2)=0
or, a=√2 since a is positive
Z=a(1+i)/√2=1+i
 
 

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