7. Consider the following statement. If the month is April, then it is spring in the Northern Hemisphere. a. Write the negation of this statement's hypothesis. b. Write the negation of the statement's conclusion c. Write the contrapositive of the statement.

1. Which set contains the number \( \pi \) ? \( \begin{array}{ll}\text { A. integers } & \text { B. rational numbers } C \text {. natural numbers } \boldsymbol{\text { D. irrational numbers }}\end{array} \)

mult. ple choice questions: choose the coriect anser from the choices for each question 1. What is the main purpose of timber conversion A) To plant more trees B) To turn logs into usable wood products C) To make paper D) To burn wood for energy

Which properties do all solids share? A. Fixed volume and fixed shape B. Color and fixed shape C. Fixed shape; volume that depends on container D. Color and fixed volume

(b) An equation in a complex number system is given by \( z=\frac{1}{\left(z_{1}-z_{2}\right)}+\frac{1}{z_{1}} \) where \( z_{1}=1+2 i \) and \( z_{2}=2-i \). Find the value of \( z \) in the Cartesian form \( a+b i \). Hence find the modulus and arguments of \( z \).

Session \( 2005 / 2006 \) 1. Given two complex numbers \( z_{1}=1+3 i \) and \( z_{2}=2-i \), express \( \frac{z_{1}+z_{2}}{z_{1} z_{2}} \) in the form of \( a+b i \), where \( a \) and \( b \) are real numbers. Hence, determine \( \left|\frac{z_{1}+z_{2}}{z_{1} z_{2}}\right| \).