Solve |2i|/|1+2|

$$\frac { | 2 i | } { | 1 + 2 | }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 2i is 2.

$$\frac{2}{|1+2|}$$

Add 1 and 2 to get 3.

$$\frac{2}{|3|}$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 3 is 3.

$$\frac{2}{3}$$

Real Part

$$\frac{2}{3} = 0.6666666666666666$$

Solution Steps

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 2i is 2.

$$Re(\frac{2}{|1+2|})$$

Add 1 and 2 to get 3.

$$Re(\frac{2}{|3|})$$

The modulus of a complex number a+bi is \sqrt{a^{2}+b^{2}}. The modulus of 3 is 3.

$$Re(\frac{2}{3})$$

The real part of \frac{2}{3} is \frac{2}{3}.

$$\frac{2}{3}$$