Solve 0.72i/0.6-1.2i

$$\frac { 0.72 i } { 0.6 - 1.2 i }$$

Evaluate

$$-0.48+0.24i$$

Solution Steps

Multiply both numerator and denominator by the complex conjugate of the denominator, 0.6+1.2i.

$$\frac{0.72i\left(0.6+1.2i\right)}{\left(0.6-1.2i\right)\left(0.6+1.2i\right)}$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{0.72i\left(0.6+1.2i\right)}{0.6^{2}-1.2^{2}i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$\frac{0.72i\left(0.6+1.2i\right)}{1.8}$$

Multiply 0.72i times 0.6+1.2i.

$$\frac{0.72i\times 0.6+0.72\times 1.2i^{2}}{1.8}$$

By definition, i^{2} is -1.

$$\frac{0.72i\times 0.6+0.72\times 1.2\left(-1\right)}{1.8}$$

Do the multiplications in 0.72i\times 0.6+0.72\times 1.2\left(-1\right). Reorder the terms.

$$\frac{-0.864+0.432i}{1.8}$$

Divide -0.864+0.432i by 1.8 to get -0.48+0.24i.

$$-0.48+0.24i$$

Real Part

$$-0.48$$

Solution Steps

Multiply both numerator and denominator of \frac{0.72i}{0.6-1.2i} by the complex conjugate of the denominator, 0.6+1.2i.

$$Re(\frac{0.72i\left(0.6+1.2i\right)}{\left(0.6-1.2i\right)\left(0.6+1.2i\right)})$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$Re(\frac{0.72i\left(0.6+1.2i\right)}{0.6^{2}-1.2^{2}i^{2}})$$

By definition, i^{2} is -1. Calculate the denominator.

$$Re(\frac{0.72i\left(0.6+1.2i\right)}{1.8})$$

Multiply 0.72i times 0.6+1.2i.

$$Re(\frac{0.72i\times 0.6+0.72\times 1.2i^{2}}{1.8})$$

By definition, i^{2} is -1.

$$Re(\frac{0.72i\times 0.6+0.72\times 1.2\left(-1\right)}{1.8})$$

Do the multiplications in 0.72i\times 0.6+0.72\times 1.2\left(-1\right). Reorder the terms.

$$Re(\frac{-0.864+0.432i}{1.8})$$

Divide -0.864+0.432i by 1.8 to get -0.48+0.24i.

$$Re(-0.48+0.24i)$$

The real part of -0.48+0.24i is -0.48.

$$-0.48$$