Solve 5/2-i+ki

$$\frac { 5 } { 2 - i } + k i$$

Evaluate

$$ik+\left(2+i\right)$$

Solution Steps

Multiply both numerator and denominator of \frac{5}{2-i} by the complex conjugate of the denominator, 2+i.

$$\frac{5\left(2+i\right)}{\left(2-i\right)\left(2+i\right)}+ki$$

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

$$\frac{5\left(2+i\right)}{2^{2}-i^{2}}+ki$$

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

$$\frac{5\left(2+i\right)}{5}+ki$$

Multiply 5 times 2+i.

$$\frac{5\times 2+5i}{5}+ki$$

Do the multiplications in 5\times 2+5i.

$$\frac{10+5i}{5}+ki$$

Divide 10+5i by 5 to get 2+i.

$$2+i+ki$$