Solve 12(-2+7i)^5+94(-2+7i)^4+859(-2+7i)^3+2587(-2+7i)^2+2039(-2+7i)-371

$$12 ( - 2 + 7 i ) ^ { 5 } + 94 ( - 2 + 7 i ) ^ { 4 } + 859 ( - 2 + 7 i ) ^ { 3 } + 2587 ( - 2 + 7 i ) ^ { 2 } + 2039 ( - 2 + 7 i ) - 371$$

Evaluate

$$0$$

Solution Steps

Calculate -2+7i to the power of 5 and get -20122+3647i.

$$12\left(-20122+3647i\right)+94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-371$$

Multiply 12 and -20122+3647i to get -241464+43764i.

$$-241464+43764i+94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-371$$

Do the additions.

$$94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i$$

Calculate -2+7i to the power of 3 and get 286-259i.

$$94\left(-2+7i\right)^{4}+859\left(286-259i\right)+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i$$

Multiply 859 and 286-259i to get 245674-222481i.

$$94\left(-2+7i\right)^{4}+\left(245674-222481i\right)+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i$$

Do the additions.

$$94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)[phone]i$$

Multiply 2039 and -2+7i to get -4078+14273i.

$$94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}+\left(-4078+14273i\right)[phone]i$$

Do the additions.

$$94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}-239-164444i$$

Calculate -2+7i to the power of 4 and get 1241+2520i.

$$94\left(1241+2520i\right)+2587\left(-2+7i\right)^{2}-239-164444i$$

Multiply 94 and 1241+2520i to get 116654+236880i.

$$116654+236880i+2587\left(-2+7i\right)^{2}-239-164444i$$

Do the additions.

$$2587\left(-2+7i\right)^{2}+116415+72436i$$

Calculate -2+7i to the power of 2 and get -45-28i.

$$2587\left(-45-28i\right)+116415+72436i$$

Multiply 2587 and -45-28i to get -116415-72436i.

$$-116415-72436i+116415+72436i$$

Do the additions.

$$0$$

Real Part

$$0$$

Solution Steps

Calculate -2+7i to the power of 5 and get -20122+3647i.

$$Re(12\left(-20122+3647i\right)+94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-371)$$

Multiply 12 and -20122+3647i to get -241464+43764i.

$$Re(-241464+43764i+94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-371)$$

Do the additions in -241464+43764i-371.

$$Re(94\left(-2+7i\right)^{4}+859\left(-2+7i\right)^{3}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i)$$

Calculate -2+7i to the power of 3 and get 286-259i.

$$Re(94\left(-2+7i\right)^{4}+859\left(286-259i\right)+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i)$$

Multiply 859 and 286-259i to get 245674-222481i.

$$Re(94\left(-2+7i\right)^{4}+\left(245674-222481i\right)+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)-241835+43764i)$$

Do the additions in 245674-222481i-241835+43764i.

$$Re(94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}+2039\left(-2+7i\right)[phone]i)$$

Multiply 2039 and -2+7i to get -4078+14273i.

$$Re(94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}+\left(-4078+14273i\right)[phone]i)$$

Do the additions in -4078+14273i+3839-178717i.

$$Re(94\left(-2+7i\right)^{4}+2587\left(-2+7i\right)^{2}-239-164444i)$$

Calculate -2+7i to the power of 4 and get 1241+2520i.

$$Re(94\left(1241+2520i\right)+2587\left(-2+7i\right)^{2}-239-164444i)$$

Multiply 94 and 1241+2520i to get 116654+236880i.

$$Re(116654+236880i+2587\left(-2+7i\right)^{2}-239-164444i)$$

Do the additions in 116654+236880i-239-164444i.

$$Re(2587\left(-2+7i\right)^{2}+116415+72436i)$$

Calculate -2+7i to the power of 2 and get -45-28i.

$$Re(2587\left(-45-28i\right)+116415+72436i)$$

Multiply 2587 and -45-28i to get -116415-72436i.

$$Re(-116415-72436i+116415+72436i)$$

Do the additions in -116415-72436i+116415+72436i.

$$Re(0)$$

The real part of 0 is 0.

$$0$$