Question

A complex number z=a+bi had an absolute value of 3.28. What could the values of a and b be ? A.a=1.5,b=1.7 C.a=1.7,b=2.8

Answer 1

The given complex number is ⇒ z = a + b i
The absolute value of z = √( a² + b² ) = 3.28
So, we will check which of the options will give 3.28

( A) IF ⇒⇒ a=1.5 and b=1.7

∴ √( a² + b² ) = √( 1.5² + 1.7²) = √5.14 ≈ 2.27

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(B) IF ⇒⇒ a=1.5 and b=3.3

∴ √( a² + b² ) = √(1.5² + 3.3²) = √13.14 ≈ 3.62

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(C) IF ⇒⇒ a=1.7 and b=2.8

∴ √( a² + b² ) = √(1.7² + 2.8²) = √10.73 ≈ 3.28

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(D) IF ⇒⇒ a=2.8 and b=3.3

∴ √( a² + b² ) = √(2.8² + 3.3²) = √18.73 ≈ 4.33
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So, the correct answer is option (C) a=1.7,b=2.8