Question

Write the expression in standard form a+bi: 4−i/2+i

a) 5/4+3/4i
b) 3/4-5/4i
c) 5/4-3/4i
d) 3/4+5/4i
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Answer 1

To write the expression in standard form a+bi, you need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator. The expression in standard form is 7/5-(2/5)i-(2/5)ia.

Step-by-step explanation:

To write the expression in standard form a+bi, we need to rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

In this case, the conjugate of 2+ia is 2-ia.

So, multiplying both the numerator and denominator by 2-ia, we get:

(4-i)(2-ia)/(2+ia)(2-ia)

Expanding the numerator and denominator, we have:

(8-4i-2ia+ia^2)/(4-2ia+2ia-ia^2)

Simplifying further, we get:

(8-4i-2ia-1)/(4+1)

(7-2i-2ia)/5

Therefore, the expression in standard form is:

7/5-(2/5)i-(2/5)ia