How to solve 77 ל 70 + ! !

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 77 ל 70 + ! ! | Equatix

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Question

$$i ^ { 72 } + i ^ { 70 } + i ^ { 67 } + i ^ { 815 }$$

Evaluate

$-2i$

Solution Steps

Calculate $i$ to the power of $72$ and get $1$.

$$1+i^{70}+i^{67}+i^{815}$$

Calculate $i$ to the power of $70$ and get $-1$.

$$1-1+i^{67}+i^{815}$$

Subtract $1$ from $1$ to get $0$.

$$i^{67}+i^{815}$$

Calculate $i$ to the power of $67$ and get $-i$.

$$-i+i^{815}$$

Calculate $i$ to the power of $815$ and get $-i$.

$$-i-i$$

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

$$-2i$$

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Real Part

$0$

Solution Steps

Calculate $i$ to the power of $72$ and get $1$.

$$Re(1+i^{70}+i^{67}+i^{815})$$

Calculate $i$ to the power of $70$ and get $-1$.

$$Re(1-1+i^{67}+i^{815})$$

Subtract $1$ from $1$ to get $0$.

$$Re(i^{67}+i^{815})$$

Calculate $i$ to the power of $67$ and get $-i$.

$$Re(-i+i^{815})$$

Calculate $i$ to the power of $815$ and get $-i$.

$$Re(-i-i)$$

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

$$Re(-2i)$$

The real part of $-2i$ is $0$.

$$0$$

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Example

Question

Evaluate

Solution Steps

Real Part

Solution Steps