The complex number $$ w $$ is given by $$ w=-\frac{1}{2}+\frac{\sqrt{3} i}{2} $$ State the modulus of wz given that $$ z=1+i $$. Select one: a. $$ \sqrt{4} $$ b. $$ \frac{\sqrt{2}}{2} $$ c. $$ \sqrt{2} $$ d. $$ \frac{1}{2} $$

Question

UpStudy AI · Accepted Answer

We begin with the property of moduli for complex numbers:
$$
|wz| = |w| \cdot |z|
$$

**Step 1: Compute $$|w|$$.**

Given 
$$
w = -\frac{1}{2} + \frac{\sqrt{3}}{2} i,
$$
the modulus is
$$
|w| = \sqrt{\left(-\frac{1}{2}\right)^2 + \left(\frac{\sqrt{3}}{2}\right)^2} = \sqrt{\frac{1}{4} + \frac{3}{4}} = \sqrt{1} = 1.
$$

**Step 2: Compute $$|z|$$.**

Given 
$$
z = 1 + i,
$$
the modulus is
$$
|z| = \sqrt{1^2 + 1^2} = \sqrt{2}.
$$

**Step 3: Compute $$|wz|$$.**

Using the property from Step 1:
$$
|wz| = |w| \cdot |z| = 1 \cdot \sqrt{2} = \sqrt{2}.
$$

Thus, the modulus of $$wz$$ is $$\sqrt{2}$$.

The correct answer is option c: $$\sqrt{2}$$.
The modulus of $$ wz $$ is $$ \sqrt{2} $$.

The complex number is given by
State the modulus of wz given that .
Select one:
a.
b.
c.
d.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Other Questions

The complex number is given by State the modulus of wz given that . Select one: a. b. c. d.