Question

The point A,B,C and D represent the complex number Z1,Z2,Z3 and Z4 and O is the origin. If OABC is a parallelogram, and Z1=1+3i and Z2=4+5i, find Z3

Answer 1

Complex numbers are divided into two parts; real and imaginary parts. The value of Z3 is $5+ 8i$

Given that:

$Z_1 = 1 + 3i$

$Z_2 = 4 + 5i$

Since O is the origin, then:

$C = OA + OB$

This means that:

$Z_3 = Z_1 + Z_2$

So, we have:

$Z_3 = 1 + 3i + 4 + 5i$

Collect like terms

$Z_3 = 1 + 4+ 3i + 5i$

$Z_3 = 5+ 8i$

Hence, complex number Z3 is $5+ 8i$

Read more about complex numbers at:

brainly.com/question/18509723