Solve 7+i/(3-4i)^2

$$\frac { 7 + i } { ( 3 - 4 i ) ^ { 2 } }$$

Evaluate

$$-\frac{73}{625}+\frac{161}{625}i=-0.1168+0.2576i$$

Solution Steps

Calculate 3-4i to the power of 2 and get -7-24i.

$$\frac{7+i}{-7-24i}$$

Multiply both numerator and denominator by the complex conjugate of the denominator, -7+24i.

$$\frac{\left(7+i\right)\left(-7+24i\right)}{\left(-7-24i\right)\left(-7+24i\right)}$$

Do the multiplications in \frac{\left(7+i\right)\left(-7+24i\right)}{\left(-7-24i\right)\left(-7+24i\right)}.

$$\frac{-73+161i}{625}$$

Divide -73+161i by 625 to get -\frac{73}{625}+\frac{161}{625}i.

$$-\frac{73}{625}+\frac{161}{625}i$$

Real Part

$$-\frac{73}{625} = -0.1168$$

Solution Steps

Calculate 3-4i to the power of 2 and get -7-24i.

$$Re(\frac{7+i}{-7-24i})$$

Multiply both numerator and denominator of \frac{7+i}{-7-24i} by the complex conjugate of the denominator, -7+24i.

$$Re(\frac{\left(7+i\right)\left(-7+24i\right)}{\left(-7-24i\right)\left(-7+24i\right)})$$

Do the multiplications in \frac{\left(7+i\right)\left(-7+24i\right)}{\left(-7-24i\right)\left(-7+24i\right)}.

$$Re(\frac{-73+161i}{625})$$

Divide -73+161i by 625 to get -\frac{73}{625}+\frac{161}{625}i.

$$Re(-\frac{73}{625}+\frac{161}{625}i)$$

The real part of -\frac{73}{625}+\frac{161}{625}i is -\frac{73}{625}.

$$-\frac{73}{625}$$