Solve 1/(3+5i)^2

$$1 / ( 3 + 5 i ) ^ { 2 }$$

Evaluate

$$-\frac{4}{289}-\frac{15}{578}i\approx -0.01384083-0.025951557i$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\frac{1}{\left(3+5i\right)^{2}}$$

To raise a power to another power, multiply the exponents.

$$\left(3+5i\right)^{2\left(-1\right)}$$

Multiply 2 times -1.

$$\left(3+5i\right)^{-2}$$

Raise 3+5i to the power -2.

$$-\frac{4}{289}-\frac{15}{578}i$$

Real Part

$$-\frac{4}{289} = -0.01384083044982699$$

Solution Steps

Calculate 3+5i to the power of 2 and get -16+30i.

$$Re(\frac{1}{-16+30i})$$

Multiply both numerator and denominator of \frac{1}{-16+30i} by the complex conjugate of the denominator, -16-30i.

$$Re(\frac{1\left(-16-30i\right)}{\left(-16+30i\right)\left(-16-30i\right)})$$

Do the multiplications in \frac{1\left(-16-30i\right)}{\left(-16+30i\right)\left(-16-30i\right)}.

$$Re(\frac{-16-30i}{1156})$$

Divide -16-30i by 1156 to get -\frac{4}{289}-\frac{15}{578}i.

$$Re(-\frac{4}{289}-\frac{15}{578}i)$$

The real part of -\frac{4}{289}-\frac{15}{578}i is -\frac{4}{289}.

$$-\frac{4}{289}$$