Question

modulus of (3+2i)/(3-2i)

Answer 1

Answer:

$\frac{\sqrt{112} }{13}$

Step-by-step explanation:

z= (3-i)/(3-2i)

First we need to rewrite the number by getting rid of the denominator.

We will multiply the numerator and denominator with (3+2i)

⇒ z= (3-i)(3+2i)/(3-2i)(3+2i)

Let us calculate each:

(3-i)(3+2i) = 9 +6i - 3i - 2i^2  

We know that i^2 = -1

⇒ (3-i)(3+2i) = 9 + 3i + 2 = 11+ 3i

⇒ (3-2i)(3+2i)= 3^2 - (2i)^2

= 9 - 4i^2

= 9 + 4= 13

therefore  (3+2i)/(3-2i)=  11/13+3/13i

therefore modulus of  (3+2i)/(3-2i)= $\sqrt{\frac{121-9}{169} }$

=$\frac{\sqrt{112} }{13}$

Answer 2

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