Naomi Hopkins

2022-04-30

Simplify $$\frac{2+2i}{4+7i}$$.

gunithd5

Beginner2022-05-01Added 8 answers

Multiply the numerator and denominator of $$\frac{2+2i}{4+7i}$$ by the conjugate of 4+7i to make the denominator real.

$$\frac{2+2i}{4+7i}\ast \frac{4-7i}{4-7i}$$

Multiply.

$$\frac{22-6i}{65}$$

Split the fraction $$\frac{22-6i}{65}$$ into two fractions.

$$\frac{22}{65}+\frac{-6i}{65}$$

Move the negative in front of the fraction.

$$\frac{22}{65}-\frac{6i}{65}$$

$$\frac{2+2i}{4+7i}\ast \frac{4-7i}{4-7i}$$

Multiply.

$$\frac{22-6i}{65}$$

Split the fraction $$\frac{22-6i}{65}$$ into two fractions.

$$\frac{22}{65}+\frac{-6i}{65}$$

Move the negative in front of the fraction.

$$\frac{22}{65}-\frac{6i}{65}$$

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