Skip to main content

Back to the full dot-point answer

TASSpecialist MathematicsQuick questions

Unit 3

Quick questions on Complex arithmetic and conjugates - TCE Mathematics Specialised (Tasmania)

3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is powers of the imaginary unit?
Show answer
The powers of ii cycle with period four: i1=ii^1 = i, i2=−1i^2 = -1, i3=−ii^3 = -i, i4=1i^4 = 1, then repeat. To simplify a high power, divide the exponent by four and use the remainder. For example i23=i20⋅i3=(i4)5⋅i3=1⋅(−i)=−ii^{23} = i^{20}\cdot i^3 = (i^4)^5 \cdot i^3 = 1 \cdot (-i) = -i.
What is the conjugate?
Show answer
Conjugates obey clean rules that examiners love to test:
What is division by realising the denominator?
Show answer
To divide, multiply numerator and denominator by the conjugate of the denominator. This turns the denominator into a real number, after which you split into real and imaginary parts.

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All Specialist MathematicsQ&A pages