** Locus of a complex number definition:**

Let** P(z)** be a property satisfied by a complex number** Z = x+ι.y. For example, **a complex number may satisfy the condition modulus of Z means **∣z∣=2**

the set

**S= {x:∣z∣=√ x²+y²=2}**

🙁 means such that)

**x:∣z∣** (means x is a set such that modulus of z)

**S= {(x, y):x²+y²}=4**

**is called the locus of the complex number** Z definition.

satisfying ∣z∣=2

**In the figure**, the** locus of z represent a circle** with **center** at (0, 0)and radius 2 (r =2)

**Locus of a complex number example:**

we fined the locus of the complex number **z = x+ι.y,**

such that for a **fixed point**

**z ₁ = x ₁ + ι y ₁, ∣z ₁- z ₂ ∣= a**

From figure, we have **→p ₒ p ₁=∣‾ p ₒ p ₁∣=∣z – z ₁∣= a**

**S = {z: ∣ z – z ₁∣ =a**

**S= {(x, y):∣x – x ₁)+ι (y – y ₁)∣=a**

**S= {(x, y):∣x – x ₁)²+ι(y-y ₁)²∣=a²**

Which is a circle with center at **Z ₁=(x ₁+y ₁) **and radius **r= a**

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