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

Complex numbers are divided into two parts; real and imaginary parts. The value of Z3 is

Given that:

Since O is the origin, then:

This means that:

So, we have:

Collect like terms

Hence, complex number Z3 is

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lol we need to see what the question is asking about

step-by-step explanation:

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°