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? (Note: i=√−1)​

Answer 1

Step-by-step explanation:

ANSWER EXPLANATION: 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)

(32)−(2i)2

Since i2=−1, this last fraction can be reduced simplified to

24+16i−3i+2

9−(−4)

=

26+13i

13

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.

Answer 2

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