Write in Standard Form (2+i)/(3i)

Problem

(2+i)/(3*i)

Solution

1. Identify the goal, which is to write the complex fraction in standard form a+b*i by eliminating the imaginary unit i from the denominator.

2. Multiply the numerator and the denominator by the conjugate of the denominator, or simply by i to make the denominator a real number.

(2+i)/(3*i)⋅i/i

3. Distribute i in the numerator and multiply the terms in the denominator.

(2*i+i2)/(3*i2)

4. Substitute i2=−1 into the expression.

(2*i−1)/(3*(−1))

5. Simplify the denominator and rearrange the terms in the numerator.

(−1+2*i)/(−3)

6. Divide each term in the numerator by the denominator to separate the real and imaginary parts.

(−1)/(−3)+(2*i)/(−3)

7. Simplify the signs to reach the final standard form.

1/3−2/3*i

Final Answer

(2+i)/(3*i)=1/3−2/3*i

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