Complex Numbers 1 Question 4

4. Let 213i3=x+iy27(i=1), where x and y are real numbers, then yx equals

(2019 Main, 11 Jan I)

(a) 91

(b) 85

(c) -85

(d) -91

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Answer:

Correct Answer: 4. (a)

Solution:

  1. We have, x+iy27=213i3=13(6+i)3

x+iy27=127(216+108i+18i2+i3)=127(198+107i)

[(a+b)3=a3+b3+3a2b+3ab2,i2=1,i3=i]

On equating real and imaginary part, we get

x=198 and y=107yx=107+198=91



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