Question

8 - i/3 - 2i If the expression above is rewritten in the form a+bi, where a and b are real numbers, what is the value of a?

Answer 1

Answer:

The required value of a = 8

Step-by-step explanation:

Here

8 - i/3 - 2i

= 8 - i(1/3 + 2)

= 8 - (7/3)i

Which is of the form a + ib

Where a = 8 & b = - 7/3

So the required value of a = 8

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Answer 2

To rewrite  8−i /3−2i  in the standard form a+bi, you need to multiply the numerator and denominator of 8−i /3−2i  by the conjugate, 3+2i. This equals

( 8−i /3−2i )( 3+2i /3+2i ) =  24+16i−3+(−i)(2i) /(3^2)−(2i)^2

which simplifies further to 2+i. Therefore, when   8−i /3−2i  is rewritten in the standard form a + bi, the value of a is 2.

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