Answer:
The values are
a = -13
b = -84
Step-by-step explanation:
Given:
z=6-7i and
[tex]z^{2}=a + bi[/tex]
To Find:
a = ?
b = ?
Solution:
Z is Complex Number consist of Real part and Imaginary part
We have
[tex]z=6-7i\\\textrm{squaring on both the side we get}\\z^{2}=(6-7i)^{2}[/tex]
Using the identity [tex](A-B)^{2} =A^{2}-2AB+ B^{2}[/tex] we get
[tex]z^{2} =6^{2}-2\times 6\times 7i+ (7i)^{2}\\z^{2} =36-84i+49i^{2}\\[/tex]
i² = -1
∴ [tex]z^{2} =36-84i+49(-1)\\z^{2} =36-49-84i\\z^{2} =-13-84i[/tex]
Now on comparing with [tex]z^{2}=a + bi[/tex] equation we get
a = -13
b = -84
