Solve 22+146/4-2i

$$\frac { 22 + 146 } { 4 - 2 i }$$

Evaluate

$$\frac{168}{5}+\frac{84}{5}i=33.6+16.8i$$

Solution Steps

Add 22 and 146 to get 168.

$$\frac{168}{4-2i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, 4+2i.

$$\frac{168\left(4+2i\right)}{\left(4-2i\right)\left(4+2i\right)}$$

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

$$\frac{168\left(4+2i\right)}{4^{2}-2^{2}i^{2}}$$

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

$$\frac{168\left(4+2i\right)}{20}$$

Multiply 168 times 4+2i.

$$\frac{168\times 4+168\times \left(2i\right)}{20}$$

Do the multiplications in 168\times 4+168\times \left(2i\right).

$$\frac{672+336i}{20}$$

Divide 672+336i by 20 to get \frac{168}{5}+\frac{84}{5}i.

$$\frac{168}{5}+\frac{84}{5}i$$

Real Part

$$\frac{168}{5} = 33\frac{3}{5} = 33.6$$

Solution Steps

Add 22 and 146 to get 168.

$$Re(\frac{168}{4-2i})$$

Multiply both numerator and denominator of \frac{168}{4-2i} by the complex conjugate of the denominator, 4+2i.

$$Re(\frac{168\left(4+2i\right)}{\left(4-2i\right)\left(4+2i\right)})$$

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

$$Re(\frac{168\left(4+2i\right)}{4^{2}-2^{2}i^{2}})$$

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

$$Re(\frac{168\left(4+2i\right)}{20})$$

Multiply 168 times 4+2i.

$$Re(\frac{168\times 4+168\times \left(2i\right)}{20})$$

Do the multiplications in 168\times 4+168\times \left(2i\right).

$$Re(\frac{672+336i}{20})$$

Divide 672+336i by 20 to get \frac{168}{5}+\frac{84}{5}i.

$$Re(\frac{168}{5}+\frac{84}{5}i)$$

The real part of \frac{168}{5}+\frac{84}{5}i is \frac{168}{5}.

$$\frac{168}{5}$$