Answer:
p = ±21
Step-by-step explanation:
Given z1 = p +2i and z2 = 1 – 2i, If |z1/z2| = 13;
|p+2i/1-21| = 13
To get p from the expression above, we need to rationalize the complex function first.
p+2i/1-21 = p+2i/1-2i * 1+2i/1+2i
= p+2pi+2i+4i²/1-4i²
Since i² = -1;
= p+2pi+2i-4/1+4
= p-4+2i(p+1)/5
= p-4/5 + 2(p+1)/5 i
Then we will take the modulus of the resulting expression and equate to the value of 13 to get p
|p+2i/1-21| = √(p-4/5)²+ (2p+2/5)² = 13
(p-4/5)²+ (2p+2/5)² = 13²
(p-4)²+(2p+2)² = 13²*5²
p²-8p+16+4p²+8p+4 = 4225
5p²+20 = 4225
5p² = 4205
p² = 841
p = ±√841
p = ±21
The possible values of p are 21 and -21
Answer:
14 cm
Step-by-step explanation:
Use pythagorean theory
a^2 + b^2 = c^2
5^2 + 12^2 = 169
square root of 169 is 13
the missing side length is 13 in
Well, you can see in the system that they give you the expression x = 6 - y. So it's literally telling you that, well, x equals (6 - y), and therefore since they're equivalent expressions, you can substitute 6 - y for x to solve the system.