+0

# question

0
119
1

For complex numbers $z$, let $f(z) = \left\{ \begin{array}{cl} z^{2}&\text{ if }z\text{ is not real}, \\ z+2 &\text{ if }z\text{ is real}. \end{array} \right.$Find $f(i)+f(1)+f(-1)+f(-i)$.

Guest Aug 29, 2017
Sort:

#1
+18829
+2

question

$$\text{For complex numbers } \\ z, \text{let } \left[f(z) = \left\{ \begin{array}{cl} z^{2}&\text{ if }z\text{ is not real}, \\ z+2 &\text{ if }z\text{ is real}. \end{array} \right.\right] \\ \text{Find } f(i)+f(1)+f(-1)+f(-i).$$

$$\begin{array}{|l|clcrc|l|} \hline z = i && f(i) = z^2 = i^2 &=& -1 && \text{(z is not real)} \\ z = 1 && f(1) = z+2 = 1+2 &=& 3 && \text{(z is real)} \\ z = -1 && f(-1) = z+2 = -1+2 &=& 1 && \text{(z is real)} \\ z = -i && f(-i) = z^2 = (-i)^2 = i^2 &=& -1 && \text{(z is not real)} \\ \hline && f(i)+f(1)+f(-1)+f(-i) = -1+3+1-1 = 2 \\ \hline \end{array}$$

heureka  Aug 30, 2017

### 9 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details