Solve left(2+iright)^4-9left(2+iright)^3+31left(2+iright)^2-49left(2+iright)+30=0

$${ \left(2+i \right) }^{ 4 } -9 { \left(2+i \right) }^{ 3 } +31 { \left(2+i \right) }^{ 2 } -49 \left( 2+i \right) +30=0$$

Verify

Solution Steps

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

$$-7+24i-9\left(2+i\right)^{3}+31\left(2+i\right)^{2}-49\left(2+i\right)+30=0$$

Calculate 2+i to the power of 3 and get 2+11i.

$$-7+24i-9\left(2+11i\right)+31\left(2+i\right)^{2}-49\left(2+i\right)+30=0$$

Multiply 9 and 2+11i to get 18+99i.

$$-7+24i-\left(18+99i\right)+31\left(2+i\right)^{2}-49\left(2+i\right)+30=0$$

Subtract 18+99i from -7+24i to get -25-75i.

$$-25-75i+31\left(2+i\right)^{2}-49\left(2+i\right)+30=0$$

Calculate 2+i to the power of 2 and get 3+4i.

$$-25-75i+31\left(3+4i\right)-49\left(2+i\right)+30=0$$

Multiply 31 and 3+4i to get 93+124i.

$$-25-75i+\left(93+124i\right)-49\left(2+i\right)+30=0$$

Add -25-75i and 93+124i to get 68+49i.

$$68+49i-49\left(2+i\right)+30=0$$

Multiply 49 and 2+i to get 98+49i.

$$68+49i-\left(98+49i\right)+30=0$$

Subtract 98+49i from 68+49i to get -30.

$$-30+30=0$$

Add -30 and 30 to get 0.

$$0=0$$

Compare 0 and 0.

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