Question

locating a power of a complex number
consider the graph of ( z ). which lettered point represents ( z^2 )?
( circ ) a
( circ ) b
( circ ) c
( circ ) d

Explanation:

Step1: Identify complex number z

From the graph, $z = 2 + i$ (2 on real axis, 1 on imaginary axis).

Step2: Expand $z^2$ using binomial rule

$$\begin{align*} z^2&=(2+i)^2\\ &=2^2 + 2(2)(i) + i^2 \end{align*}$$

Step3: Simplify using $i^2=-1$

$$\begin{align*} z^2&=4 + 4i - 1\\ &=3 + 4i \end{align*}$$

Step4: Match to graph point

$3 + 4i$ corresponds to point C (3 on real axis, 4 on imaginary axis).

Answer:

C. Point C