Question

5. (2+2+3+3 marks) (a) Find $|(1 + i)(1+2i)(1+3i)|$. (b) Find $(1+\sqrt{3}i)^{100}$. (c) Find the set of all the complex numbers z such that $|z - i| = |z| + 1$. (d) Let D = \{$z \in \mathbb{C} : 1 \le |z| \le 2$, $0 \le \text{Arg}(z) \le \pi\}$. Find f(D), where f: $\mathbb{C} \to \mathbb{C}$ is defined as f(z) = 1/z$^2$.

          5. (2+2+3+3 marks) (a) Find $|(1 + i)(1+2i)(1+3i)|$.
(b) Find $(1+\sqrt{3}i)^{100}$.
(c) Find the set of all the complex numbers z such that $|z - i| = |z| + 1$.
(d) Let D = \{$z \in \mathbb{C} : 1 \le |z| \le 2$, $0 \le \text{Arg}(z) \le \pi\}$. Find f(D), where
f: $\mathbb{C} \to \mathbb{C}$ is defined as f(z) = 1/z$^2$.

$5. (2+2+3+3 marks) (a) Find |(1 + i)(1+2i)(1+3i)|. (b) Find (1+√(3)i)^100. (c) Find the set of all the complex numbers z such that |z - i| = |z| + 1. (d) Let D = {z ∈ℂ : 1 ≤ |z| ≤ 2, 0 ≤Arg(z) ≤π}. Find f(D), where f: ℂ→ℂ is defined as f(z) = 1/z^2.$

Added by Jessica B.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Gaurav Kalra

06/11/2023

Step 1

Step 1: To find |(1+i)(1+2i)(1+3i)|, first multiply the complex numbers together. Show more…

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5. (2+2+3+3 marks) (a) Find|(1+i)(1+2i)(1+3i)| (b) Find (1+ V3i)100 (c) Find the set of all the complex numbers z such that |z - i|= |z[+ 1. (d) Let D={z e C:1<|z|< 20< Arg(z)< T}. Find f(D),where f : C - C is defined as f(z) = 1/z2.