Solve 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

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

Evaluate

$1+4i$

Solution Steps

Calculate $i$ to the power of $2$ and get $-1$.

$$2\left(-1\right)+6i^{3}+3i^{16}-6i^{19}+4i^{25}$$

Multiply $2$ and $-1$ to get $-2$.

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

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

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

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

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

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

$$-2-6i+3\times 1-6i^{19}+4i^{25}$$

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

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

Do the additions in $-2-6i+3$.

$$1-6i-6i^{19}+4i^{25}$$

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

$$1-6i-6\left(-i\right)+4i^{25}$$

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

$$1-6i-\left(-6i\right)+4i^{25}$$

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

$$1-6i+6i+4i^{25}$$

Add $1-6i$ and $6i$ to get $1$.

$$1+4i^{25}$$

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

$$1+4i$$

Real Part

$1$

Solution Steps

Calculate $i$ to the power of $2$ and get $-1$.

$$Re(2\left(-1\right)+6i^{3}+3i^{16}-6i^{19}+4i^{25})$$

Multiply $2$ and $-1$ to get $-2$.

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

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

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

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

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

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

$$Re(-2-6i+3\times 1-6i^{19}+4i^{25})$$

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

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

Do the additions in $-2-6i+3$.

$$Re(1-6i-6i^{19}+4i^{25})$$

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

$$Re(1-6i-6\left(-i\right)+4i^{25})$$

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

$$Re(1-6i-\left(-6i\right)+4i^{25})$$

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

$$Re(1-6i+6i+4i^{25})$$

Add $1-6i$ and $6i$ to get $1$.

$$Re(1+4i^{25})$$

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

$$Re(1+4i)$$

The real part of $1+4i$ is $1$.

$$1$$