Solve 1/2(2i)+9-1/5(10i)+2

$$\frac { 1 } { 2 } ( 2 i ) + 9 - \frac { 1 } { 5 } ( 10 i ) + 2$$

Evaluate

$$11-i$$

Solution Steps

Multiply \frac{1}{2} and 2i to get i.

$$i+9-\frac{1}{5}\times \left(10i\right)+2$$

Multiply \frac{1}{5} and 10i to get 2i.

$$i+9-2i+2$$

Combine the real and imaginary parts in i+9-2i.

$$9+\left(1-2\right)i+2$$

Add 1 to -2.

$$9-i+2$$

Combine the real and imaginary parts.

$$9+2-i$$

Add 9 to 2.

$$11-i$$

Real Part

$$11$$

Solution Steps

Multiply \frac{1}{2} and 2i to get i.

$$Re(i+9-\frac{1}{5}\times \left(10i\right)+2)$$

Multiply \frac{1}{5} and 10i to get 2i.

$$Re(i+9-2i+2)$$

Combine the real and imaginary parts in i+9-2i.

$$Re(9+\left(1-2\right)i+2)$$

Add 1 to -2.

$$Re(9-i+2)$$

Combine the real and imaginary parts in 9-i+2.

$$Re(9+2-i)$$

Add 9 to 2.

$$Re(11-i)$$

The real part of 11-i is 11.

$$11$$