Solve E=(1+i)^4/(1-i)^7

$$E = \frac { ( 1 + i ) ^ { 4 } } { ( 1 - i ) ^ { 7 } }$$

Solve for E

$$E=-\frac{1}{4}+\frac{1}{4}i=-0.25+0.25i$$

Steps for Solving Linear Equation

Calculate 1+i to the power of 4 and get -4.

$$E=\frac{-4}{\left(1-i\right)^{7}}$$

Calculate 1-i to the power of 7 and get 8+8i.

$$E=\frac{-4}{8+8i}$$

Multiply both numerator and denominator of \frac{-4}{8+8i} by the complex conjugate of the denominator, 8-8i.

$$E=\frac{-4\left(8-8i\right)}{\left(8+8i\right)\left(8-8i\right)}$$

Do the multiplications in \frac{-4\left(8-8i\right)}{\left(8+8i\right)\left(8-8i\right)}.

$$E=\frac{-32+32i}{128}$$

Divide -32+32i by 128 to get -\frac{1}{4}+\frac{1}{4}i.

$$E=-\frac{1}{4}+\frac{1}{4}i$$

Assign E

$$E≔-\frac{1}{4}+\frac{1}{4}i$$