Solve () Simplify 2i ^ 2 + 6i ^ 3 + 3i ^ 16 - 6i ^ 19 + 4i ^ 25 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$2 i ^ { 3 } + 6 i ^ { 3 } + 3 i ^ { 16 } - 6 i ^ { 19 } + 4 i ^ { 25 }$$

Evaluate

$3+2i$

Solution Steps

Calculate $i$ to the power of $3$ and get $-i$.

$$2\left(-i\right)+6i^{3}+3i^{16}-6i^{19}+4i^{25}$$

Multiply $2$ and $-i$ to get $-2i$.

$$-2i+6i^{3}+3i^{16}-6i^{19}+4i^{25}$$

Calculate $i$ to the power of $3$ and get $-i$.

$$-2i+6\left(-i\right)+3i^{16}-6i^{19}+4i^{25}$$

Multiply $6$ and $-i$ to get $-6i$.

$$-2i-6i+3i^{16}-6i^{19}+4i^{25}$$

Subtract $6i$ from $-2i$ to get $-8i$.

$$-8i+3i^{16}-6i^{19}+4i^{25}$$

Calculate $i$ to the power of $16$ and get $1$.

$$-8i+3\times 1-6i^{19}+4i^{25}$$

Multiply $3$ and $1$ to get $3$.

$$-8i+3-6i^{19}+4i^{25}$$

Calculate $i$ to the power of $19$ and get $-i$.

$$-8i+3-6\left(-i\right)+4i^{25}$$

Multiply $6$ and $-i$ to get $-6i$.

$$-8i+3-\left(-6i\right)+4i^{25}$$

The opposite of $-6i$ is $6i$.

$$-8i+3+6i+4i^{25}$$

Do the additions.

$$4i^{25}+3-2i$$

Calculate $i$ to the power of $25$ and get $i$.

$$4i+3-2i$$

Do the additions.

$$3+2i$$

Real Part

$3$

Solution Steps

Calculate $i$ to the power of $3$ and get $-i$.

$$Re(2\left(-i\right)+6i^{3}+3i^{16}-6i^{19}+4i^{25})$$

Multiply $2$ and $-i$ to get $-2i$.

$$Re(-2i+6i^{3}+3i^{16}-6i^{19}+4i^{25})$$

Calculate $i$ to the power of $3$ and get $-i$.

$$Re(-2i+6\left(-i\right)+3i^{16}-6i^{19}+4i^{25})$$

Multiply $6$ and $-i$ to get $-6i$.

$$Re(-2i-6i+3i^{16}-6i^{19}+4i^{25})$$

Subtract $6i$ from $-2i$ to get $-8i$.

$$Re(-8i+3i^{16}-6i^{19}+4i^{25})$$

Calculate $i$ to the power of $16$ and get $1$.

$$Re(-8i+3\times 1-6i^{19}+4i^{25})$$

Multiply $3$ and $1$ to get $3$.

$$Re(-8i+3-6i^{19}+4i^{25})$$

Calculate $i$ to the power of $19$ and get $-i$.

$$Re(-8i+3-6\left(-i\right)+4i^{25})$$

Multiply $6$ and $-i$ to get $-6i$.

$$Re(-8i+3-\left(-6i\right)+4i^{25})$$

The opposite of $-6i$ is $6i$.

$$Re(-8i+3+6i+4i^{25})$$

Do the additions in $-8i+3+6i$.

$$Re(4i^{25}+3-2i)$$

Calculate $i$ to the power of $25$ and get $i$.

$$Re(4i+3-2i)$$

Do the additions in $4i+3-2i$.

$$Re(3+2i)$$

The real part of $3+2i$ is $3$.

$$3$$