If imaginary part of multiplicative inverse of 2+3i3+2i is −ab, where a and b are coprime numbers, then
A
b−a=8
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B
a+b=−8
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C
a+b=13
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D
b−a=18
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Solution
The correct option is Ab−a=8 Let the multiplicative inverse be Z Z×2+3i3+2i=1⇒Z=12+3i3+2i⇒Z=3+2i2+3i×2−3i2−3i⇒Z=6−9i+4i−6i222−(3i)2⇒Z=12−5i13⇒Im(Z)=−513∴a=5,b=13a+b=18,b−a=8