Write in Standard Form 2/(2-15i)

Problem

2/(2−15*i)

Solution

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

2. Multiply the numerator and the denominator by the conjugate of the denominator, which is 2 + 15i$.

2/(2−15*i)⋅(2+15*i)/(2+15*i)

3. Distribute the numerator and use the difference of squares pattern for the denominator.

(2*(2+15*i))/(2−(15*i)2)

4. Simplify the denominator by applying the identity i2=−1

(4+30*i)/(4−225*(−1))

5. Combine the terms in the denominator.

(4+30*i)/(4+225)

(4+30*i)/229

6. Separate the fraction into its real and imaginary parts to reach standard form.

4/229+30/229*i

Final Answer

2/(2−15*i)=4/229+30/229*i

Want more problems? Check here!