Pls expert help in question no 7 7 If x+iy=4+4i5+12ithen 169(x2+y2)2 is 1) 5 2) 10 3) - Maths - Complex Numbers and Quadratic Equations

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Pls expert help in question no 7

7 If x + i y = 4 + 4 i 5 + 12 i t h e n   169 ( x 2 + y 2 ) 2
  i s
1) 5
2) 10
3) 25

Neha Sethi · Accepted Answer

Dear student
We have,x+iy=3+4i5+12iSquaring both sides, we getx+iy2=3+4i5+12i⇒x2-y2+2ixy=3+4i5+12i×5-12i5-12i⇒x2-y2+2ixy=15-36i+20i-48i225-144i2⇒x2-y2+2ixy=63-16i169⇒x2-y2+2ixy=63169-i16169On comparing, we getx2-y2=63169 and 2xy=16169Now, x2+y22=x2-y22+4x2y2⇒ x2+y22=631692+161692⇒ x2+y22=11692632+162⇒169 x2+y22=11693969+256⇒169x2+y22=4225169⇒169x2+y22=25Note:1) i2=-12) a±b2=a2+b2±2ab
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Pls expert help in question no. 7 7. If x + i y = 4 + 4 i 5 + 12 i t h e n 169 ( x 2 + y 2 ) 2 i s 1) 5 2) 10 3) 25

Pls expert help in question no. 7

7. If $x + i y = \sqrt{\frac{4 + 4 i}{5 + 12 i}} t h e n 169 (x^{2} + y^{2})^{2} i s$
1) 5
2) 10
3) 25