Let z = (11-3i) ÷ 1 + i . If a is a real number such that z - ia is real, then the value of a is :
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Let z = (11-3i) ÷ 1 + i . If a is a real number such that z - ia is real, then the value of a is :
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Given z = (11-3i)/(1+i)
Multiply numerator and denominator with (1-i)
z = (11-3i)(1-i)/(1+i)(1-i)
= (11-3i-11i-3)/(1+1)
= (8-14i)/2
= 4-7i
z-ia = 4-7i-ia
z-ia real means imaginary part is zero.
-7-a = 0
a = -7
Hence option (4) is the answer.
Verified answer
Answer:
a = - 7
Used Method :
i) Rationalising for integral denominator
ii) Any complex number is real
That implies Im(z) = 0